All quilts are blankets, but not all blankets are quilts. Project Linus (at least from what I'm familiar with) accepts all handmade blankets - be they quilts, fleece "no-tie" blankets, or knitted/crocheted afghans.
It's a rule of logic. All dogs are mammals, but not all mammals are dogs. All cats are mammals, but not all mammals are cats. Does that make all cats dogs and all dogs cats? Nope. So since all quilts are blankets and all afghans are blankets, that does not make all quilts afghans and all afghans quilts. So blanket would be the appropriate term.