A breakdown diagram of the military branches of the Adeptus Mechanicus.

From left to right, to the best of my knowledge:

Centurio Ordinatus: The vehicles and war machines of the Tech Priests are maintained by this branch.

Auxilia Myrmidon: An organisation made up of those Priests who specialise in knowledge directly related to engaging in battle. Easily the smallest branch here, but if you see a Tech Priest leading an army with an absurd number of huge guns directly hardwired to his body instead of overseeing the field from a hover platform or the safety of an orbital command station he’s probably one of these dudes.

Skitarii: The tech guard. Footsoldiers of the Forge Worlds, differentiated from Imperial Guard mainly by augmented bodies and access to superior equipment.

Legio Cybernetica: Everyone is a cyborg in the Mechanicus. The difference with these guys is that they’ve been augmented into massive lumbering war machines.

Ordo Reductor: Specialists in maintaining and deploying ancient technology humanity doesn’t remember how to build.

Collegia Titanica: The Imperial organisation in charge of deploying Titans and one of the top reasons not to fuck with the Mechanicus.

Also of note is that they’re heavily involved with the Imperial Knight houses, supplying and maintaining their equipment whilst carefully encouraging their loyalty to Mars over Terra.