Canvas. For me canvas is a general term I use to discribe just about any painting surface I use to paint on. In reality only part of the time do I use canvas or to be more exact cotton canvas. Let see I have used stretched cotton canvas (either pre-stretched or stretched by me). To stretch canvas you wrap it around stretcher bars which typically are made of wood.
In recent years a newer type of canvas has come out on the market. It goes by several different names like, gallery wrap, studio wrap, museum edge and creative edge, just to name a few. But they are all basically the same thing.
The canvas is stretched from the front clear around the sides and fastened in the back. Thus leaving the front and sides to be painted on. Plus these types of canvases tend to be deeper thus giving the artist more room to paint. I've seen them go as deep as six inches, looking more like a box then a panel. Plus because the sides are painted there is no need to frame these paintings. Thus saving money on not framing.
Another type of option is canvas board. Where canvas is adhered to a board.
There are many different cloths you can paint on after they have been primed with gesso. The two I prefer are cotton or linen, with linen being my favorite. I like the interesting and unique variety of textures linen creates with out being too rough. Now my mentor Greg Olsen is a bit more brave then I am. He has painted on all sorts of surfaces, from silk, to polyester, plaster (which he carved first to make it a relief carving then painted it), wood panels and hardboard (both having done paintings on the smooth side and rough side). Also to add more tooth (texture) to the painting surface you can add some marble dust to your gesso. A small amount is like 200 grit sand paper and a large amount it like 20 grit (Greg has also add so much marble dust to one of his paintings that the gesso was like very think paste. So he sculpted it into trees and rocks for a relief like sculpture and then painted it too). I like a very smooth surface, so needless to say these approaches to surface texture do not appeal to me.