Consul
Legiones Consularis, or Consuls, were a rank bestowed to Space Marines during the Great Crusade and Horus Heresy. They were not Legion Consuls, which were specifically tasked with keeping order in the Legions. They were identified by their specialization in many esoteric arts of combat and war. Called upon to use their mastered arts when their Legion needed them, with the outbreak of the Horus Heresy these officers would face their grandest trial. As one can imagine, there is a metric shit ton of different variants of Consuls.
Variants
Consul Champion
The predecessor to the Company and Chapter Champions of the Chapters, their role has seen the least amount of change. After all, the Champion was always meant to be an exemplary swordsman among their brothers and fight the greatest foes. How else were they to improve that?
Consul Chaplain
While the Imperial Cult was not established yet, there were still people who needed to shout really loudly to inspire zealous anger. Similar to their successors in black and bone, these chaplains would inspire hatred in their charges and wield a master-crafted Power Weapon - though unlike the Crozius Arcanum synonymous with the later iterations, these could be any sort of power weapons than merely mauls.
Speaker of the Dead
Before the VI Legion had Wolf Priests mixing Fenrisian Lore with the Imperial Creed, the Speakers of the Dead were the resident apothecaries-slash-cult leaders of the lesser deity Morkai.
In the tabletop, this not only gave an attached unit Hatred (Everything) and Stubborn, but they also gained a Narthecium and a master-crafted power maul in place of the Crozius they would later gain.
Consul Delegatus
In smaller conflicts where the Legion's top command would deem the situation to minor to directly intervene, they would deputize a lesser officer, typically a Centurion, with full command of their own army. These officers would then assemble their own strike forces to lead into battle.
In the tabletop game, the Delegatus is an upgrade that offers no special equipment, but it does grant the Consul the Master of the Legion rule, and thus the ability to qualify as the warlord in smaller games as well as the ability to select a Rite of War as if they were a Praetor. They also get a single-use ability to roll a Leadership Check to force any units that were falling back or pinned to rally and act normally for the turn.
Consul Forge Lord
Though trained on Mars in the ways of the Mechanicum, unlike the Praevians the Forge Lords are selected for their incredible skill with machinery. While they may have made use with the war machines of the Mechanicum, their preferences usually led them more to repairing the Legions armoured forces. As with their successors, these Forge Lords were usually the anchors to lead all the production within the legions.
On the Horus Heresy tabletop, Forge Lords were given their servo-harnesses to help them repair their vehicles as well as being useful multi-weapons. On top of this, they could also purchase Cortex Controllers, which would prove particularly useful if they also decide to ally with any automata on the field, including the Thallax maniples that they unlock access to.
Consul Librarian
Due to the Council of Nikaea, the Librarius was dissolved among the legions, but as many can attest, this was not for long.
In most cases, there may have been cases where a Psyker was elevated to a more senior position to make use of their unnatural powers, but as time passed, it became clear that the powers of psykers were one of the only ways to defeat the foul warpspawn that the traitors summoned...or to summon them. Following the Heresy War, Guilliman would re-establish the Librarius as a structure in the Chapters.
As with their future successors, these Librarians would have access to Force Weapons with which to channel their psychic powers. Psychic Hoods did exist in this era in order to help cancel out any harmful psychic influences, but they were not so common that they could be issued to any Librarian that wanted one.
Consul Esoterist
Among the psykers of the legion, only a growing few of them dared to dive deeper into the unknown fields of Warpcraft, but it proved to be incredibly effective, if in varying ways. While the loyalist legions had Esoterists who studied how to banish daemons outright, the traitor legions discovered ways with which they could summon the forces of Neverborn into reality with their own power.
Esoterists are a specialization that only appeared with the rebooted Horus Heresy tabletop game, and by all means, they are identical to Librarians with two exceptions - one is access to Archaeotech Pistols, but the bigger one is their own unique Anathemata psychic discipline, which is inaccessible by any other way.
Caster of Runes
Before they were called Rune Priests, the Casters of Runes were the standing psychic force of the VI Legion. Of course, they were deemed "exceptions" to the ban on Librarians due to claiming their powers were derived from shamanism and channeling the spirit of their homeworld of Fenris.
Practically, aside from their limited choice in psychic powers (including some of their own), they were identical to Librarians.
Stormseer
Similar to the VI Legion, the Stormseers of the V Legion were also treated as special "exceptions" to the no-Librarians rule due to being shamans, though the Stormseers weren't so hypocritical as to reject the Librarius as a failed structure. These Stormseers would persist after the Heresy and effectively become the Librarius for the chapter.
Practically, aside from their limited choice in psychic powers (including some of their own), they were identical to Librarians.
Consul Praevian
The Consul Praevian was a type of Astartes commander during the Great Crusade and Horus Heresy and a variant of the Consul.
Trained on Mars by the Mechanicum these commanders were the keeper of the Legion's robots, including Battle-Automata given honorary induction into the Legion's ranks. On the field of battle they marched at the forefront of Battle-Automata forces, guiding them through the engagement.
They were often chosen from Veterans whose injuries required extensive Bionics. Known to be solitary individuals, they rarely advanced up the chain of command. Some Legions used the rank as a dumping ground for warriors seen as unfit for other duties. However, in the Iron Hands (No surprise there) and Salamanders, the rank was seen as a great honour. On the traitor side, Iron Warriors also make great use of them due to their command over siege robots. As they are heavily augmented, they wore what is essentially Artificer Armour for defence, but by the time of Horus' clusterfuck benanza some of them had to wear Mark V: Heresy Armour.
Some has considered viewing them as a predecessor of the Techmarine, but with each of them in command of a mini robot-army.
On the Horus Heresy tabletop, they are the Master of the Legion's Automata. He is a Support Officer, so cannot be used as a compulsory HQ and thus cannot be in an allied contingent. Comes equipped with a Cortex Controller, Cortex Designator and can't take anything that makes him bulky. First, you choose a type of Battle Automata (only Castellax and Vorax at this time) to accompany him, forming one unit with MCs (so he can't go to ground) that he can't leave. Any time the Praevian hits an enemy unit with a ranged attack, he grants Preferred Enemy to the Automata in his unit for that turn (so give him a bolter). Upgrade them with Enhanced Targeting Arrays for 2+ re-rollable accuracy for your weapons.
The original Praevians of the Forge World Black Books were unique in that they not only treated their charges as members of the legion, but they could also equip them with special equipment that might have proved useful to them.
Legion Primus Nullificator
As the Heresy ground on, the Loyalists tried a great many methods to ward off the daemons. One of these would be the Nullificators, a small force of marines who adorned their power armour with Hexagrammatic Wards and used superstition and normally unsanctioned weapons like disintegrators. Leading these forces would be the Primus Nullificators, psykers who would be specially trained to purge daemons.
Paladin of the Hekatonystika
The I Legion was known for its labyrinthine orders and chambers, an anomalous organization that made it impenetrable to outsiders but allowed them to draw from countless experiences when needed. Among these are the Hekatonystika, an order shrouded in extreme secrecy but uniquely experienced in a special art of warfare. A Paladin may on occasion be assigned from the orders of the Inner Circle to take the lead in a situation where the order's experience would prove absolutely necessary.
The Paladin of the Hekatonystika is a unique consul introduced in the Liber Astartes of the HH tabletop reboot, given a Terranic Greatsword and can select one of the choices for the Orders of the Hekatonystika given to the Inner Circle Knights Cenobium. With the bump to Leadership and WS as well as Stubborn, one could see the Paladin as an improved Consul Champion, though not honour-bound to accept any challenges.