There are a bunch of different styles of swing dance but they seem to have a lot in common with each other, even though the moves and footwork and everything differs considerably between them. This seems to be a list (the second section, "Basic Swing Dances").
Swing dance organizations in Toronto I've heard of are Toronto Swing Dance Society, Bees Knees Dance (teaching), University of Toronto Swing Dance Club.
Recently I've been trying rockabilly jive, which I'm not sure how it quite fits into the above or whether it's called a type of swing dance or not. It's not to be confused with "jive" itself, which is a variant on East Coast Swing dance. Here's a video of some people dancing in a way I couldn't even hope to aspire to.
Unlike in Scottish Country Dance and the other dance forms mentioned in the first paragraph of this page, swing dance is about improvisation, and I'm not really good at improvising on the spot like that. In Scottish Country Dance you may not dance perfectly of course, but there's something you're supposed to do, and you're trying to do exactly that. That form of dance is more amenable to me.