Heat death means [in simple form] that matter reaches a temperature below which it ceases to interact with other matter in a way that produces new chemical reactions.

Dead stars and old planets can still collide together, but you probably wouldn't expect things to grow and explode, or shrink, or exchange molecules, or whatever else they do now that makes the universe "heat live". I don't know if that helps give a better picture. Heat death is, effectively, the density/temperature below which molecules stop doing their thing with each other, though they may retain their last known formation. [Molecules are the rather involved collections of atoms, if you recall fifth grade chemistry].

Reaching absolute zero is a different thing, that is the point at which atoms no longer have any motion whatsoever and atoms themselves fall apart.

Heat death, then, is the point at which the density and/or temperature of the universe means the various parts stop interacting, but atoms and random molecules still float about randomly. Gravity still works. Some lumps will be bigger than other lumps. Absolute zero means even electrons and protons fall off their respective atoms, and that is not currently thought to be a point the universe can reach without outside assistance.