I assumed that Nerds have a broader base; i.e. they're fans of, say, "video games" or "board games" or whatever, while Geeks are extremely obsessive about a single topic, say, "World of Warcraft." It's a specific vs. broad thing.
And I think you can't really overlook the idea that Nerd has a connotation of being generally academic, while Geek has a connotation of being just dorky. One is a statement of intelligence and sometimes social competence, while the other is all about social competence and doesn't comment on the intellect.