Undead is the description given to those that have died, but have continued to exist. The majority of Undead are imprisoned and sent to the Undead Asylum to await their doom.
Hollow is the description given to those Undead that have lost their sanity and sense of self; those Undead that were once friendly to the player's character, for instance, will instead attack on sight. The time taken to go Hollow is dependent on the individual, and their (as well as the player's) actions.