Imperial Worlds
Agri-Worlds
Agri-Worlds are planets in the Imperium of Man entirely dedicated to agriculture. A typical agri-world is mostly covered by millions of square kilometers of farmland managed by a few million farmers and a couple of spaceport cities/transportation hubs where stuff is loaded onto starships to be sent elsewhere to feed the Imperium's teeming masses. Said ships also drop off huge loads of shit (sometimes literally) to keep things fertile. Others are ocean worlds with huge fish farms or gas giants with habitable zones with balloon bases that collect airborne plankton that gets mashed into Soylens Viridens. Their tithes are paid in grain, space potatoes and grox, which, combined with their relatively sparse population, means that they rarely have to raise regiments for the Imperial Guard.
Cemetery World
Extremely depressing worlds that are dedicated almost entirely to being huge graveyards.
Civilized Worlds
Civilized worlds are the 'normal' inhabited planets in the Imperium. Lacking hives or forgeworld scale factories they never the less have a decent level of technology and a population in the same ballpark as modern earth.
Death Worlds
Death Worlds are worlds where everything is hostile to Human Life. And that means everything. The animals, the plants, sometimes even the very air itself is fatal for humans, while being just habitable enough to warrant colonization. Examples include Catachan and the majority of Astartes homeworlds.
Feral Worlds
Feral Worlds are places where mankind has regressed to the level of the Stone Age.
Feudal Worlds
Feudal Worlds are planets abandoned by the greater human species during the Age of Strife and for one reason or another regressed back to 1000 A.D to 1500 A.D technologies. They are also generally divided into small kingdoms which fight with each other but pay tribute to the Imperium. Because apparently the Neo-Medieval themes of 40k just weren't enough so they had to add in several actual medieval-themed worlds too. The Imperium deliberately keeps them from progressing further technologically with only a small handful of exceptions, since the Imperium already works on a form of the feudal system anyway. More importantly, it ensures that the planet's citizens know their place in Imperial society and don't get any ideas about secession into their heads. But the big reason why these planets are kept around is because they provide good light infantry for the Imperial Guard and space marines like to recruit from there.
Forge World
The Imperium's massive workshops. Forge Worlds are planets dedicated entirely to Industry and the property of the Adeptus Mechanicus.
Hive World
Pleasure World
Pleasure worlds are essentially tourist traps and vacation spots IN SPEEEHS, and are predictably restricted to the exclusive use of nobles, senior officials of the Adeptus Terra, and other big shots in the Imperium.
Tithe Astartes (Space Marine) Worlds
These are planets claimed by a Space Marine chapter. While typically most Chapters select Death Worlds, Feral Worlds, or Feudal Worlds as a home due to the hardiness of their residents, some of these planets are more civilized or even at a better standard of living than most of the Imperium- the Realm of Ultramar is an obvious example of the latter.
Tithe Astartes planets are notable for being one of only two planet types exempt from the Imperial Tithe, with the only other type being Aptus Non (read: planets which have been Exterminatus'd)
War Worlds
Planets locked in eternal war. So what makes these planets different from just any old planet with a war on it? Scale and length. Generations of soldiers have lived and died. Some planets, as well, just have such warlike cultures that even without an external force, they will kill each other (not necessarily for khorne, usually planets with scarce resources result in this, since the best way to deal with limited supplies is to kill someone else and take their stuff).
For the most part, these are probably pretty shitty places to grow up in, even by Imperial standards.
Dead Worlds
Exterminatus isn't the only way planets die. Ecological disaster, sudden celestial events, alien invasion, someone disengaged from the warp too close to the planet and accidentally the atmosphere... Keep in mind, unlike the entry below, these aren't strictly forbidden for colonization, its just the work required to make it habitable involve either completely isolated arcologies or some way of making the planet habitable again. The Tyranids, after they nom all the life on the planet, will then turn to draining the planet of its core, atmosphere and any water still remaining before setting off for new real estate.
Quarantine/Forbidden Worlds
While it seems cut and dry what kind of planet this is, these tend to have a large spectrum of why they are blocked off and how it is enforced. For the most part, the reason is heresy, the planet has fallen to xenos influence, worships chaos, broke off from the imperium. Others include perceived danger. A planet being a death world is one thing, but if the last five colonization attempts on a planet ended with the inhabitants mysteriously vanishing, the imperium is going to block it for settling and generally tell the inquisition to figure out what is going on.