The definitions I grew up with were that a geek is someone unusually into something (so you could have computer geeks, baseball geeks, theater geeks, etc) and nerds are (often awkward) science, math, or computer geeks. But definitions vary.

"Geeks and Nerds", by Randall Munroe, licensed under Creative Commons Attribution-NonCommercial 2.5 License

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The definitions I grew up with were that a geek is someone unusually into something (so you could have computer geeks, baseball geeks, theater geeks, etc) and nerds are (often awkward) science, math, or computer geeks. But definitions vary.