There are sevral types of zombies in the Felneyverse, depending on both which story you are reading, and which universe it takes place in.

Type 1 - Bacterial

Created by bacteria, they completely infest a body and "quroum sense". The ones in the brain use it's signals to control the muscles. Destroying the brain "kills" the zombie, but the body might continue squirming for a while. Also the tissues are infectious.

Type 1a - vampires

A very exacting dose of the zombie bacteria creates a "vampire". These are really zombies who retain their intelligence (but still have an unstoppable drive to propagate the infection). They can also continue to appear alive by obtaining fresh blood, and heal wounds. They have to have their brains destroyed to stay dead, like any other zombie. The exacting dose is very hard to administer deliberately, never mind get by accident. Too little, and the person's immune system fights it off, too much, and they just become a normal zombie.

Type 1b - super zombies

An extremely large dose of the zombie serum can create one of these. They can run fast, rapidly heal wounds, and also their tissues are rearranged into calcified "armour" (using bone tissue, the skeleton and muscles are replaced by zombie bacteria itself). They also grow long, razor-sharp claws.

Type 2 - Spider-created

These zombies were in the original (no longer canon) version of The Gun. They are created by a type of large spider, which clings on to it's victim's head (after they died), and spreads tentacles through out the body to reanimate and control them. The zombies retain some former knowledge (including the ability to speak, and of who killed them). They can also be ordered about, especially if they were soldiers in a previous life, and are "used to" following orders. They also grow long claws, have glowing eyes, super speed, super strength, rapid healing, and the body needs to be completely destroyed to kill them (or maybe killing the spider will do it, I never explored the concept much).

Type 3 - Voodoo-created

These are scientifico-magical zombies, created by rituals involving mind-altering drugs and hynosis. Eventually they are administered a drug that suppresses life signs and brings about paralysis. They later get dug up from their graves and obey orders given to them by whoever they have been hypnotised to see as their master.

There may also be stories in the Delta universe etc, where the magical aspect is played up a bit more - but still ultimately based in science. The magic powder will have defined properties, even if those break the laws of physics or biochemistry in more conventional universes

Type 4 - Magical

Zombies created by pure magic. May act like type 1, 2 or 3, depending on the story.

Type 5 - Demonic

Essentially the same as bacterial, only the plague is magically spread (but through the same vectors). These zombies were created by Satan to infest hell, and torment the souls that were sent there. These souls may occasionally be given a physical body, then be fed to zombies. Or they may become zombies, and made to murder their loved ones, if they have also been sent to hell. They behave the same way as Type 1 zombies, and thus the same way as those in the Romero films, because Satan saw a bootleg copy of Night of the Living Dead once, and thought it was "really fucking metal".