I must say, "trekkie" and "trekker" evoked images in me of people going to conventions, wearing Vulcan ears there, reading and buying all there is in the franchise their money permits to, and all that. I'm not saying that if you are doing any (or all) of these things, I consider you as such, it's just the stereotypical image I have with the term. (Neither am I saying I think there's anything 'wrong' with doing these things.)
I myself love rewatching episodes of the old series, and philosophising a bit on this board to nourish my inner geek, but that's the extent of it. I'd call myself a 'star trek fan' if I'd have to give it any name. I might even go to a convention once, just to see what the experience is actually like- but as of yet have never done so.