Full Idea
There is the question of the identity of a person over or across time ('diachronic' personal identity), and there is also the question of what makes for personal identity at a time ('synchronic' personal identity).
Gist of Idea
Personal identity is a problem across time (diachronic) and at an instant (synchronic)
Source
E.J. Lowe (Locke on Human Understanding [1995], Ch.5)
Book Reference
Lowe,E.J.: 'Locke on Human Understanding' [Routledge 2004], p.103
A Reaction
This seems to me to be the first and most important distinction in the philosophy of personal identity, and they regularly get run together. Locke, for example, has an account of synchronic identity, which is often ignored. It applies to objects too.