It depends on source. From real historican sources (modern mythologies/urban legends), to ancient mythologies, fantasy etc.
The mage, who transform is "soul" or hearth into another item (eg. egg, or vial etc...) doesn't have to be lich. On behalf of other undeads, it again depends on style. And type of undead. Some are just moving flesh (abnomination), animated by magic and with realy restricted inteligence, maybe weak daemon from another plane of existence. The same could be for some skeletons and zombies. Other are true undeads, returned from plane of dead. Eg. by strong magic and bounded with leash, commanded by strong necromancer. Or those, who are just returned by some event (eg. evocation/invocation, don't know, whichever is right for this event, that mean summoned by necromancer, but unbound, without leash, eg. undead was too powerfull etc.; strong residual magic or that dead person have strong will to do just some erand or there was ritual, that bounded its soul to body, so it would never leave it in first place...)
I don't think that W3 is good source of information in first place.