It's a bit of an explaination.
One of the original zombie movies is George Romero's "Night of the Living Dead". In that movie the recently dead were returning to life, but had no intelligence, bascially animals with just instincts to walk around and eat.
That movie was created by George Romero and John Russo. However, the pair had a falling out, and they each created their own sequals. The stipulations were that Romero's films would be referred to as the "the dead" films. (Night of the Living Dead, Dawn of, Day of, Land of, Diary of, Survival of,)
Romero's films tend to be straight horror films and his zombies didn't talk. In his films, the brains are reactivated, and the zombies eat flesh. If the brain is destroyed, the zombie is killed, so if a zombie eats someone's brains, their body can't reanimate.
For John Russo, his stipulation was his set of sequals would contain the terms "Living Dead". (Return of the Living Dead, Return of the Living Dead 2).
Russo's films were more of a comedy/horror combination. They often featured slapstick situations, and his zombies were capable of limited speech, most often moaning "braaaaaains". In his films the zombies strictly ate the brains, but somehow the bodies would reanimate without the brains, which makes no sense.
When it comes to I Zombie, this show is based on a comic book that follows Russo's storyline, but takes it further. The young girl who is a zomibe has retained all of her intelligence. She gets a job in the morgue so she has access to brains without killing anyone. In the end she helps crimefighters because when she eats the brain, she can see the memories of the human the brain belonged to, often revealing the identity of the person who murdered them.
Most horror movie fans consider Romero's films classics and the true cannon. Russo's films are considered 'unoffical' zombie movies.