There are lots of different kinds of zombies in movies, which you could read more about in one of the links above. Some are reanimated corpses, some are infected by some sort of virus, etc. Some are slow, some are fast. Some eat brains, some eat flesh, some drink blood, etc. They may have qualities of zombies crossed with something else, like vampires, demons, etc. Many of them are never called zombies in the movies in which they appear. In fact, the creators of some movies may take pains to specify that they're definitely not zombies. Still, audiences will often call anything that seems like zombies, "zombies," no matter what the creators (or characters in the movies) say about it. So... whatever. Here I'll just list any movies with monsters commonly considered zombies. I guess. I should also say some zombie movies are serious horror, and some are comedy.
Note, some anthology webseries that I've seen include short films about zombies, among many other subjects:
Bloody Cuts ("Mother Died", "Zombie Dating")
Totally Real Movies Coming Soon ("Snackpocalypse")