Got a couple of minutes to kill before computer class starts, so here I am!
When I was in high school...back in the Stone Age...the 80s, that is...is when terms like "nerd" and "geek" were first born and being regularly applied to people. I can's speak to how they evolved into their use today, but back then it seemed we ascribed "nerd" to someone who was smart, got really good grades, was not so much a mover or shaker in the social world but had reasonable social skills--IF you had the vocabulary to keep up with what they were saying to you!! They were maybe more oriented toward science and math and computers, but got good grades all around.
Geeks, on the other hand, were maybe equally smart, but not necessarily. Their geekly status was determined by comparatively lacking social skills, an obsession with Star Wars or Star Trek (though others may have liked these franchises, the geeks were fanatically out there and in your face about it), and fashion sense and often hygiene were worse than questionable.
The big dividing line: Nerds would eventually get dates and have sex if they weren't already (usually with other nerds), but with geeks this prospect got more and more dubious as time progressed.