Traditionally, lenses wider than 24mm on full-frame are "ultra-wide". On a smaller-sensor Canon DSLR, a 15mm lens provides that same field of view (16mm on Nikon, Pentax, or Sony; 12mm on Olympus/Panasonic). So on an APS-C camera, a 20mm lens would be "wide" but not "ultra-wide" — but with the increased field of view of full frame, that would fall under ultra-wide.
On full frame, a 35mm lens is wide angle (but not ultra-wide); that same lens would be "normal" on an APS-C camera.
In either case, yes, the 18-55mm kit lens is a wide-angle lens. On a crop-factor DSLR, that nicely covers a reasonably wide angle, through normal, up to a moderate "portrait-length" telephoto.
(On some systems, some lenses designed for APS-C cameras won't work at all on full frame. Or, they'll work but with poor performance in the corners — and on Nikon, for example, this is compensated-for by automatically cropping-out the edges when a designed-for-APS-C lens is attached. But it's pretty much universal that full-frame lenses will work on APS-C.)