I am a geek in the sense of the word. I game, I read all the time, I enjoy many geeky shows, and stuff like that.
Definition of a nerd: what makes someone a nerd is how passionate they are about something and how they will try to understand that thing on a granular level, like, more than anyone else in the world. And a lot of times, at the expense of things that they probably should be doing. Like, if you're blowing off work to make sure that scale model that you're building is perfect, that's nerdy. So I think it's the level of which someone has a passion and focus about something that they care about, I think that's what it is.