It is unknown if the Living Dead are so named because they are actually dead creatures that have been reanimated in some form, or if they merely resemble the conventional definition of "undead". In the Harry Potter universe, truly reviving the dead is usually stated to be impossible.
The only two confirmed creatures to be considered part of this group are Vampires and Zombies. Whether other creatures like Inferi or ghosts would be considered Living Dead as well is unknown.
In LEGO Harry Potter releases, skeletons are referred to as "walking dead," but it is uncertain if this is equivalent to "living dead."