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.
The Buddhist Pali word 'birth' ('jati') refers to the arising of the self-view of 'a being' ('satta').
And what is birth? The birth of the various beings into the various orders of beings... SN 12.2
'A being,' lord. 'A being'. To what extent is one said to be 'a being'? Any desire, passion, delight or craving for form... feeling... perception... fabrications... consciousness: when one is caught up there, tied up there, one is said to be 'a being.' SN 23.3
Why now do you assume 'a being'? Have you grasped a view? Just as with an assemblage of parts, the word 'chariot' is used, when the aggregates are present, there is the verbal convention of 'a being.' SN 5.10
The many different Pali words translated as 're-birth' essentially refer to the re-arising or re-formation of the self-view of 'a being' due to kamma (action).
For example, under the influence of self-view, a person undertakes a financial scam & celebrates when they become or are 're-born' financially wealthy. Then, when they are imprisoned for fraud, the same person is re-born as a prisoner in a jail & are unhappy.
In summary, despite the different interpretations, 'rebirth' is always a doctrine of 'moral efficacy'.
Where as 'reincarnation' is always a metaphysical doctrine of the soul or some other mental substance entering a new physical body.
A Buddhist can believe in moral 'rebirth' but not believe in 'reincarnation' (life after death).
Reincarnation involves a soul that transmigrates. A soul is the five aggregates minus physical form.
Rebirth is like lighting one candle with another candle. The stream of consciousness, a.k.a life force, continues from one existence to another but the remainder of the five aggregates; form, perception, sensations and mental formations (which would stay together during a reincarnation of a soul); dissipate.
Rebirth is when a soul leaves the body in the state of ignorance and then again gets a new body in ignorance. Reincarnation is when soul leaves the body in full knowledge and such souls reincarnate only to fulfill a some mission or purpose in life.