To me, a general SF convention is an event like BayCon, OryCon, Norwescon, Loscon, Westercon, or Worldcon. The primary purpose of SF conventions are for fans of the genre to meet and talk with other fans and, as Ben Yalow put it very well at OryCon, to "continue the discussion" that started about 80 years ago. I am obviously a stuck-up elitist literary snob, because I'm being told that Dragon*Con is what a general-interest convention should be.
In essence, science fiction and fantasy has become so mainstream that those of us who consider ourselves SF fans in an older tradition have been completely passed by and are in a literary backwater that actually respects written words and think that's where the roots of the genre are, whereas the majority of people equate SF & F with movies and television and are probably all-but-unaware of the older tradition.