Nerd: you are very smart perhaps in all things or one thing whether it is math or art history but very social inept i.e. unable to hold conversations with people outside of work and school type conversations. You are unable to dumb down explanations of your field of expertise and do not comprehend that people may not be at your level in that field.

Geek: You are very smart perhaps in all things or one thing whether it is math or art history but you are able to socialize with people well and hold conversations. You are able to speak to nerds in your field but also able to speak to "lay people" in your field because of your ability to explain in terms other than those in your field of expertise.

If that makes sense. :)