The term canvas serves as a generic term for any fabric that’s used as a support for painting. The fabric can be cotton duck (the most common), linen (a more expensive choice regarded as superior), or a synthetic fiber (uncommon). Find out more about what your choices are when it comes to canvas for painting.
Cotton duck canvas has nothing do to with ducks but it is the most common and the cheapest painting canvas. It comes in various weights (thicknesses) and weaves (how tight the individual threads are woven). The cheapest cotton canvases are loosely woven and the fabric can easily distort when stretched if you’re not careful. If you’re stretching your own cotton canvas, you may even find it cheaper in a fabric store than an art supplies store.
You can fill in the indentations in the weave with primer or gesso to create a smoother painting surface (especially if you apply multiple layers, sanding down each time). Or you can use the weave of the canvas as part of the texture of your painting.