There are a lot of names for the advanced Type Three reanimate. Most common is "Kappa" - arising from a misunderstanding about the Greek alphabet. It does not in fact go ABC - alpha-beta-kappa like English. To be fair, even a long time resident of Athens would be hard pressed to concentrate on letter order if they ran across one of these things.
Ones are normal people back from the dead, and one theory holds an Alpha is what happens when they remember part of who they used to be. (Not a theory I espouse, mind you - but it does raise some interesting question of could there be an Alpha-plus with further recall. That is beyond the scope of my reports for now.) Type Twos were the sick and injured with excess nano-vac inside them, and are rebuilt strangely. Three's are cybernetic zombies, raised to the strength of the titanium artificial limbs rather than the calcium bone...
Perhaps it would be better to say the gulf between base and advanced is a matter of limits, and exceeding them. A basic corpse moving after brain death shouldn't have any notable intelligence - an Alpha surpasses that. Two is reconstructed, Beta improved in more grotesque ways. Threes integrate machinery into the reanimation process, but are still human in form.
A Gamma no longer relies simply on the human form and the materials present within it at the time of reanimation - instead it actively assimilates from the environment, and grows. Most of the reports so far claim they retain a general humanoid shape, if somewhat resembling a power armor or alien encounter suit that any normal person. Rumors abound though, that when the bipedal stance can no longer support their weight, they can adopt to something else. What these new forms might be vary from tales of "gun-toting zombie elephants" to tanks merged with human flesh. Although both of these outcomes seem unlikely, all reports do agree that the Gamma merges with ranged weapons making them the only reanimate to consistently be able to fight at a distance. (Alphas might use firearms, but it is unlikely.)
Gammas seem to be the only type of reanimate that shows a territorial preference. They seem only to be found in cities, or large complexes like mega-structures and industrial parks. Within these places, they are truly king and queens - the broken sight lines and narrow terrain greatly complicates the placement and use of the kinds of heavy weapons needed to kill one of these monsters. Meanwhile, it gives the Gamma plenty of places to hide for ambush or escape.