Is there a legit definition to both?
Probably not, but my mom and I sussed it all out one day:
Nerd = someone with strong intellectual interests. It really has nothing to do with physical attractiveness, athletic prowess or social comfort levels. Bill Clinton is a nerd - during the 1992 campaign, before the womanizing scandal hit, all anyone could talk about was him being a Rhodes scholar and a detail oriented policy wonk. As we all know he's also a mack daddy and wildly charming. At the same time, Al Gore is also a nerd - no macking to be had, and not so much with the charming.
Geek = someone who is passionately interested in a particular subject. Again, no one is really knocked out of the geek category by being attractive or athletic. And, just about everyone is a geek about something. I know garden geeks and birding geeks who are just as freaky when they geek out about their beloved subject as any computer geek ever was.
Note: To "geek out" is to talk at length about your beloved subject whether the person you are talking to is interested or not. To not notice that you are causing someone to glaze over moves you closer to the final category:
Dork = a dork is usually not atheltically gifted, has little to no sexual appeal and is mostly distiguished by a high level of social awkwardness.
Now - where things get confusing is that, while you can be a nerd or a geek and not be a dork, a large percentage of nerds and geeks
are dorks, and geeks of certain types, such as comic book geeks, sci fi geeks, computer geeks, etc have enough geek/ dork cross-over for a stereotype to have formed in the public consciousness. But trust me, I work in museums so everyone I know is a nerd - some are charming, some make out like bandits and some are so painfully dorky you run when you see them coming.