What is the difference between rebirth and reincarnation? In my readings of Buddhist commentary there is a distinction drawn between rebirth and reincarnation. But to me it is unclear what is the difference between rebirth and reincarnation--the explanations are rather abstruse. Is there a simple one-sentence explanation of this difference?
Reincarnation implies a soul that takes a body; rebirth does not, so it is preferred.

Note that neither term has a widely used cognate in the Pali texts, perhaps because the concept of "re-" anything implies the continuation of an entity. Buddhism tends to talk about birth and death in a more linear fashion; rather than being reborn, it's "being born again" (e.g. dukkhā jāti punappunaṃ).

Further, the focus in Buddhism is on individual mind states and ultimate reality rather than the conceptual reality of birth and death, so it's not really a core teaching. Death is a concept; at the moment of a being's death, one body/mind experience ceases and the next one arises, just as it did through the entire life.