The two biggest themes to be called "classic" are "classic space" and "classic castle" and refer to the period when these themes were first introduced.
Brickset subthemes reflect this: Classic Castle covers the first yellow castle and accessories, from 1978 to 1983. I'd tend to include the new series from 1984 myself, since there wasn't much to speak of before that, but maybe I'm just wrong or maybe that only shows that there is no actual definition of "classic" to speak of.
The brickset subtheme for Classic Space covers the period from 1978 to 1987, with one extra set in 1988. Afterwards, they started naming themes, such as Futuron or Space Police, so you could say that the classic period covered the space sets before that. A lot of fans seem to limit themselves to the "blue with gray wings" livery of the first space sets, though, and do a fantastic job of it.
There's also a castle fan community site called Classic-Castle.com and several Classic space fan community sites, such as Neo Classic Space (notice the blue-and-gray again). I think there was once a classic-space.com but that doesn't seem to be operational any longer.
By extension, I suppose all themes from the same period qualify too. Bear in mind that this period (the eighties, in a nutshell) correspond to the period when most of nowadays AFOLs were kids, so they have fond memories of the sets they had or drooled about. But as far as I know, none have devoted fanbases; and there are no corresponding "Classic City" or "Classic Technic" subthemes on brickset.
Saying "Classic Jack Stone" will probably get you very puzzled and/or angry looks.
These words are used to lure in collectors who really want the "exclusive" stuff. It probably means that they don't really use that many new complicated pieces, making it classic. The winter specials, such as the house, post office, toy shop, etc...
The word "vintage" means, of, relating to, or denoting wine of high quality: "vintage claret". Another word for this is "wine". Wine is aged. So are these LEGO sets. this means that the LEGO set will only be sold for a limited time, while also being a classic LEGO set. It really means "old". If you search "vintage LEGO" it will come up with a bunch of really old LEGO sets that are classics and very old.