I don't hear of liches mentioned that often. The two examples I remember (Oblivion and Adventure Time) portrayed liches as zombies with magical powers.
That's not
entirely inaccurate. In general, a lich is a powerful spellcaster that uses arcane means to live beyond death. They store their essence/soul in a magical phylactery, trapping it in the mortal world. So long as the phylactery remains intact, they cannot be truly destroyed, as their body will be restored in time. As such, given the tremendous magical power needed to become one at all, a lich's phylactery tends to be exceedingly well protected.
What tends to separate them from zombies (aside from the rather obvious aspect of retaining their minds) is that while zombies tend to rot, liches are generally just more... dried out. Their flesh preserved rather like a mummy's.