Fan, Or Geek?

Yesterday I was speaking with someone who said, “Shakespeare fans, or as you call them, geeks.”
I don’t think it’s quite that easy.  I think there’s a difference, I’m just not sure I can explain it.   I know plenty of Red Sox fans, for example, but I’ve never heard some one call themselves a Red Sox Geek.
From where I sit it goes something like this.  A Shakespeare fan knows that there’s Shakespeare on Boston Common, so he goes to see the show.  Likes it, maybe talks about it over dinner with the friends that came with.  A geek wears his Shakespeare t-shirt with a joke very few people will get, live tweets the show, looks for other “geeks” in the audience to bond with (like those that brought Othello to Othello?), and goes home afterward to get on the blogs and talk about the show, and any other topics that come up tangentially, as long as the conversation will continue.
Maybe the distinction lies there, in social circle?  I could be a Shakespeare fan entirely by myself.  I don’t need to hang out with other Shakespeare fans.  I can just read it, see it, like it.  Done.  But I’m not like that, I’m a geek about it.  I needed an outlet for my love of the subject, and when I couldn’t find one, I made one.  And what I’ve found in the intervening years is that fellow geeks have flocked here for the same reasons.
Or, getting back to the sports thing I mentioned earlier, perhaps there is still some level of academic association with the term, confused so often with “nerd” as it is.  Star Wars geek, math geek, theatre geek.  Since I’m clearly on this side o the line I can’t really speak to the other side – anybody want to step up and proclaim themselves a marathon geek or a weightlifting geek?
What do you folks think?  When asked, in the real world, are you a fan or a geek? How would you explain it?