Trekkie is a fan of the old series. They might like TNG, DS9, or Voyager, but they started as TOS fans and usually still like that best. I believe the name comes from the hippie-like utopian Star Trek universe. Trekkie sounds similarish to hippie.

Trekkers like TNG, DS9, and/or Voyager best, or at least became Trek fans from watching them.

I'm a Trekker because I like DS9 best and because DS9 was what first got me into Trek. Most Trekkies are older than your average Trekker, 'cause they were around when TOS was on TV.