Living Dead is a blanket term for various films and series that all originated with the seminal 1968 zombie movie Night of the Living Dead created by George A. Romero and John A. Russo.
After the film's initial success, the two creators split in disagreement regarding where the series should go and a contract was drawn up. Any future Romero films would lose the "Living" prefix and simply be referred to as Dead movies and Russo, who wanted to branch the series off into literary territory, would retain the rights to "Living Dead" (though fans nevertheless refer to Romero's as Living Dead films). Thus, both series would be considered canon and each would be able to do what they liked with the continuity of the projects.
ROMERO'S DEAD SERIES
Labeled Trilogy of the Dead until Land of the Dead, this is considered by most fans as the one true series. Each film is laden with social commentary on topics ranging from racism to consumerism. The films are not produced as direct follow-ups from one another. The films' only continuation is the epidemic of the living dead, the situation advancing with each film, but with different characters and even moving the time ahead from the last to the time in which they were filmed despite the world's progression being the only interlocking aspect of the series. They are different stories telling how different people react to the same phenomenon ranging from citizens to cops to army officials and back again. There are no real happy endings to the films as each takes places in a world that has gotten worse since the last time we saw it, the number of zombies ever increasing and the fate of the small amount remaining living always in the balance.