My wife is a quilter. For those who don't know a quilt consists of a four components, a pieced together "top" (this would be all the t-shirts sewed together with a border to separate them and a exterior border). The middle section is either cotton or synthetic "batting" material, and the back is once again most times a pieced together and corresponds to the top pattern (t-shirts in this case) bottom would be a map of the top, or the back of the t-shirts if the top was the front of shirt) but can be a single large piece of material. These three pieces are fastened together to create a "quilt" by either hand (very cool but unbelievably time consuming) or by a machine, some of which now have computer designs that can be used. This procedure is either done in a constasting color thread or a color that blends in. Then a contrasting material color is used to "band" all the way around the edges and seal the three pieces together. Costly and time consuming.
A blanket is one piece of material, no top, no middle, no back, just a piece of warm cloth. You sew two blankets together, you still have a blanket. Quilt has to have the pieced together pattern.