Not sure, but I think woven fusibles are heavier and more often used in tailoring and dressmaking. Non-woven fusibles are the kind most often used by quilters -- Wonder Under, Steam-a-Seam, etc.
There is one other type I know of, fusible tricot. This is a knit fusible -- one of the best choices for making a t-shirt quilt because the t-shirt fabric remains pliable and the fusible doesn't make it too stiff or heavy. T-shirt fabric is knit, so using a knit fusible with it makes sense.