Okay, so I think this is a point of confusion.
The term “zombie” is both a technical term, referring to a family, and a common name, referring to a genus.
The family Zombie is a broad, overarching group that includes the genus that many people call zombie (Ghoulus, not to be confused with Ghouli, the unrelated genus of the Ghala family which also includes bogeymen and some ghosts*) as well as the Mummy genus (Pyrima), the spore-zombie genus (Fungan) and a few others.
The colloquial term “Zombie” is the common term for the genus Ghoulus, which is in the family Zombie and includes Ghoulus romero (the walking zombie), Ghoulus snydera (the running zombie), and Ghoulus smithi (the vampiric zombie, also called the legendary zombie).
Interestingly, there are several things called “zombies” that are neither Ghoulus nor Zombie, including the dancing zombie (Jacksoni thrillera), which is more closely related to (although not currently actually in the same family as) clowns.
*Note: the ghosts in the Ghala family are not true ghosts. True ghosts are in the order Spectere, which is entirely unrelated to Ghouli, Ghoulus, Pyrima, and Fungan. Ghala “ghosts” are given the common name ghost because of their superficial similarity to true ghosts.
Important note: sometimes you’ll see people claiming that zombies are domesticated! They are not! Some zombies can be tamed (like Ghoulus romero), but zombies are wild animals and might hurt you if you approach them! Leave them alone and don’t feed them!