As far as I've seen, the general opinion seems to be that a geek is someone with particular skill in a special area, e.g. computing, whereas nerd is a derogatory term for rather obsessive and often socially dysfunctional people. There seems to be less differentiation between younger people (particularly people at my school) compared to older people who I know, and it is from the older people I know that this clearer idea of the difference comes.
N.B. Following research on urbandictionary.com, this seems to be the opposite way round in america.
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