Abhuman
Abhuman (from ab-, "of, from, away from," human) is a term used in the Imperium of Man to refer to a stable-breeding subspecies of humanity. Although their physiology and mentality would be so different that they should technically be classified as a whole different species, all together. Officially, they are not considered mutants by virtue of their breed stability, but they are generally not treated the same way as "normal" humans. Civilian abhumans are almost always an underclass on other worlds, and when Imperial Guard regiments are raised from abhuman worlds as part of the Imperial Tithe they tend to be broken up into individual companies, platoons, or squads that are then attached to other regiments as auxiliary troops. Though, this is usually because most abhumans that qualify for Guard service are either too stupid, too undisciplined, too specialized, or aren't numerous enough to maintain their own independent regiments.
So far as is known, none of the abhuman strains below are compatible with Space Marine implants, while all are compatible with the Psyker gene.
Origins
Humanity's characteristics are influenced by the conditions in which it grew up, including gravity, climate, and diet. If a population were isolated in a different environment for a long enough time, their distant descendants would be adapted to those new conditions.
During the Dark Age of Technology, humanity spread to the stars, first with slower-than-light colony ships, and then with Warp drives after the discovery of the Navigators. Some of their destination planets were very different from Earth, and when humanity entered the Age of Strife, the inhabitants of these worlds were cut off from other colonies; when contact was restored during the Great Crusade (or even later), their gene pools had diverged so far from the baseline that they could almost be classified as separate species. The Imperium spared them, though, because while they were clearly not pure humans, they were useful and no more prone to mutation than any other human. As humanity had ready access to genetic engineering in that era, it can be difficult to distinguish natural evolution from artificial enhancement in many cases, as Games Workshop does not usually reveal the necessary details.
The Horus Heresy novels mentioned that even during the high point of abhuman tolerance, formerly human populations have been purged due to achieving certain (high) levels of genetic "deviancy". The natives of Davin were shaggy creatures that were close to it, though Chaos may have had a hand in that, unbeknown to the Imperials.
Abhumans can be loosely categorized by the nature of their origin.
Definitely Artificial
These abhumans are definitively known to have been manufactured at some point. In the case of the Afriel Strain and Gland War Veterans, though, their actual status as true abhumans is a bit iffy, as it's unclear just how many of their augmented traits (if any) are genetically transferrable, and their populations are closer to (dwindling) engineered batches rather than self-sustaining breeds.
Homo navigo
Navigators are a three-eyed, specialized group of psykers that helps guide Imperial Ships through the Warp (in fact, they were developed to enable Warp travel); although essentially vital for the Imperium's survival, some radical groups in the Imperium declare them to be heretical mutants. These guys are so different from the mainstream human, that they are actually classified as another species of the Human genus, and not a human subspecies, hence their scientific name. They also get their own house in the Houses of Terra within the Terran Administratum, which provides a large modicum of independent political clout within the Imperium and prevents them from being sacrificed to the Golden Throne.
Navigators are never any other kind of psyker (including being a Blank).
Afriel Strains
Homo sapiens superior (Presumed)
Afriel Strains were the byproduct of the Imperium trying to create the 'Ultimate Human' via a shadowy experimental process which used genetic material from a number of the Imperium's greatest heroes to, in effect, make clones of them. While this may sound Awesome in theory, the Strains themselves...seem to suffer a severe case of bad luck. The amount of genetic tempering has effectively made the Afriel Strain a new sub-species of human. Whether they are allowed to do their 'business' and see whether the genes can pass on is unknown.
Despite this, the Afriel Strain project is still approved by the Imperium, by and large, and is still undergoing improvements to fix the...issue.
Gland War Veterans
Homo sapiens tyranicavenatorus (Presumed)
Similar to the Afriel Strains, Gland War Veterans were humans that underwent severe genetic tempering to effectively combat and out-adapt the Tyranids. The term 'Gland War Veterans' is sometimes shortened to Glandies or Gland Warriors; they were made by the Mechanicus of the Biologis Magi in order to create a new human sub-species to effectively kill Tyranids without needing to waste more human lives.
While still in its experimental phase, the Tech Priests in charge are already looking forward in making more of them and further improving on their combat effectiveness.
Probably Natural
These abhumans are extremely adapted for one specific world, which is how evolution works; one would expect the Dark Age of Technology to be capable of far more versatile adaptations. Typically, the only details we are given about them is their planet of origin.
Felinids
Homo sapiens hirsutus
Thanks to 6th Edition, Imperial catgirls are canon! They're found only on the planet Carlos McConnell and we know absolutely nothing about them whatsoever... Which is quite disappointing really. Judging by the Latin name, they are likely furries.
Troths
Homo sapiens verdantus
Only found on the world of Verdant; no other details known.
Neandors
Homo sapiens hyannothus
Only found on the world of Hyannoth IV; no other details known.
Scalies
Homo sauromimus (Presumed)
Scalies are what happens when you mix an Ogryn with a Crocodile and launch the abomination down the deepest toilet hole. They often populate the underhive of Hive Worlds and are frequent bodyguards of Scavvies which are just poor hobos. They are so genetically unstable that their vox boxes have essentially twisted beyond proper human speech, only communicating via grunts or growls. Seriously, they are so far from the norm that they barely register as human, let alone a separate genetic caste.
They are like Killer Croc from Batman. Each of them can regenerate their limbs like a reptile if it is chopped off. They aren't fielded by the Imperial Guard due to their inability to effectively communicate and somewhat heretical mutations.
While they are found on many, distinct planets, they are only found in Hives, all of whom probably produce very similar waste, which the Scalies live in; combined with their lack of "stability" (i.e. having Scalies from different planets reliably breed true), they are what one would expect of natural evolution in an artificially similar environment.
Probably Artificial
These abhumans are adapted for a wide variety of worlds, and, critically, were found on multiple, distinct worlds; as evolution has an astronomically poor chance of producing results like this, odds are far better that the native population, in order to deal with problems brought about by the Age of Strife, genetically tampered with themselves to survive, explaining why populations on similar but distant worlds would arrive at identical (or very similar) solutions.
Longshanks
Homo sapiens longatus
Longshanks are adapted for very low or zero gravity, such as would be expected on a damaged voidship. In appearance, the Longshanks are bald with very pronounced eyes and have unnaturally long legs, when compared with baseline humans. May be an entire race of gingers if their name is any indication. Recently reappeared in the canon to be taken captive by orks and then summarily executed by their space marine rescuers for being mutants.
Ogryn
Homo sapiens gigantus (sapiens being used in the loosest sense of the word)
Ogryn are transparently based on the archetypal fantasy ogre: big, strong, and dumb. They are useful as Imperial Guard shock troops because they are big enough to wreck the enemy and dumb enough to charge on command. They are resolutely loyal to their immediate superior officer, but this also makes it extremely easy to turn them to serving Chaos, as they will perform any command given to them if their commanders are persuasive enough, though their childlike faith in the God Emperor makes outright corrupting them harder.
Ogryn hail from high gravity worlds, where their large size is a major limiting factor (smaller creatures are much, much better at lifting more weight relative to their own, and everything is heavier on a high-gravity planet, including an organism's own body). As even a relatively small amount of time to genetically drift would inevitably cause them to shrink (due to extreme selection for minimizing height) and become more intelligent (they are routinely described as far too stupid to farm and probably too stupid to hunt, even though their large size drastically increases their food demands), the implication is that someone or some thing (such as the guard population or planetary AI) has been inducing their large size and low intelligence to help keep them contained and suffering. Their adaptations make them naturally suitable for cold, low-gravity worlds, although their low intelligence makes them unlikely to thrive in any environment where they are responsible for feeding, sheltering, and/or clothing themselves.
Ratlings
Homo sapiens minimus
Ratlings used to be space halflings, but the latest edition miniatures give them hairy bare feet, making them look more like space hobbits (though both archetypes have a fair amount of overlap). They are also noted kleptomaniacs, so they've got some space kender in them, too. Their good eyesight and small size make them useful as snipers, but they are otherwise useless in a fight and their personal characteristics make them less than endearing to Imperial Guard leadership, though the Guardsmen themselves usually don't mind -- they are perfectly fine with trading with Ratlings for some special equipment or extra rations, and they're well-known as the sorts of field cooks that can make three old rats, a handful of sawdust, and a stolen muddy boot taste downright edible. Also, they tend to shag like bunnies.
Taken together, their adaptations make them excellent at surviving on hot, high-gravity worlds with scarce access to food, particularly a damaged voidship, where they would also be adapted to tight living quarters.
Squats
Homo sapiens rotundus
Squats grew up on high-gravity mineral-rich worlds near the core of the galaxy, and became adapted to be short, robustly built, and adept miners. If this sounds familiar, it's because they were intentionally designed to be the space-equivalent of Dwarfs from Warhammer Fantasy Battle.
They were introduced in the First Edition of Warhammer 40,000 as a separate army to the various Imperial forces (being fiercely independent), and were mentioned sparingly thereafter, until they were written out of the background (hence the term "squatted"), but the sixth edition rulebook has written them back in again.
They are morphologically very similar to Ratlings but have the inferior eyesight one would expect of a race adapted to low-light and/or interior conditions (where nothing to be looked at is ever very far away), as well as the increased musculature and robustness to be expected of an environment more naturally abundant in food (that is, where Ratlings seem to be more adapted to hunting and gathering, Squats are more adapted to farming).
Nightsiders
Homo sapiens nocturnus (Presumed)
Nightsiders are abhumans adapted to live in the dark; not much else is known about them. They may have any of the adaptations one might expect in a low-light environment, such as overly large eyes to gather as much light as possible or vestigial eyes that have given up on sight altogether, and/or enhanced alternative senses to cope, such as sonar. As almost all dark environments are also cold, odds are very good they have some solution for this, as well, although this could be anything from thick, insulating fat and/or hair to having natural access to the Psyker discipline of Pyromancy, similar to how Navigators are stable psykers.
Pelagers
Homo sapiens oceanus
Abhumans adapted for Ocean Worlds; possibly an attempt to bring back the Saharduin, like the Demiurg are an attempt to bring back the Squats.
Unknown
Beastmen
Homo sapiens variatus
Beastmen are on their way to being declared mutants; as it is, the Adeptus Arbites has basically declared them an underclass, preventing them from traveling to most planets and excluding them from the Imperial Guard unless they're willing to be cannon fodder- something which many of them view as their chance to atone for the crime of being born as mutants. This will probably be for the best, since their Warhammer Fantasy Battle counterparts are one of the major parts of the armies of Chaos, but one wonders if the 40K beastmen would be less likely to fall to Chaos if the Imperium made them feel just a little welcome.
All Beastmen which have not been mutated by Chaos are morphologically similar, having a basic human body type modified to have the head and lower legs of a cloven-hoofed, ruminant mammal from Earth; one can assume they also possess internal changes, such as a 4-chambered stomach. However, they exhibit widespread diversity within that category, leading to their common consideration of being mutants. As these adaptations "merely" adapt the organism to being better at running and jumping while sacrificing proficiency at climbing and being able to digest cellulose, but Beastmen are found on many worlds throughout the Imperium, they would seem to be artificial if not for the fact that one would expect far better of the Dark Age of Technology than, for example, needing to include horns in order to accomplish digesting grass. Their most likely origin is being artificial but not for the standard reason (like Ogryn seem to be), in particular due to possible interference by nonhumans, such as Chaos or Dark Eldar, both of whom are notorious for genetically tampering with human populations for their own ends.