Full Idea
When psychologists discuss identity, they are typically concerned with the kind of person someone is, or wants to be (as in an 'identity crisis'). But when philosophers discuss identity, it is numerical identity they mean.
Gist of Idea
Psychologists are interested in identity as a type of person, but philosophers study numerical identity
Source
Derek Parfit (The Unimportance of Identity [1995], p.293)
Book Reference
'Personal Identity', ed/tr. Martin,R /Barresi,J [Blackwells 2003], p.293
A Reaction
I think it is important to note that the philosophical problem breaks down into two areas: whether I have numerical identity with myself over time, and whether other people have it. It may be that two different sets of criteria will emerge.