I have this conversation SO OFTEN!!! My friends and myself fall somewhere on the geek/nerd spectum... but many of them get offended if you call them "nerds" whereas to me I don't see it as insulting, but they seem to think that been called a "nerd" means that you have no social skills
I'm really not sure on the difference as it seems to depend on who you sppeak to and it's hard to put into words... but as an example we were playing D&D the other week (instantly ont he geek spectrum there lol) and the GM was describing a pit, so I decided the best thing to do was to drop a stone down it to see how deep it was, and they allowed this and told us how long it took. At this point most the group nodded and said "fairl'y deep then", but 2 of us grabbed a pen and paper and did the maths to work out hwo deep it would be... by my logic that makes us 2 more on the nerdy side whereas the rest (who mocked us for this) are on the geeky side. Same occurs with conversations about certain games and comics, most will just discuss them whereas I will be able to cite exact aspects, publications and dates of things which puts me on the nerd side again...
I also have conversations in binary on facebook...

which even I am slightly ashamed of for it's nerdyness and lack of a lifeness lol