fusable interfacing is a different product from paper backed fusable where both sides are adhered to fabric-
fusable interfacing has a fusable added to one side of it-
when you want a finished edge on appliques you can place a fusable interfacing on top of the shape (right sides together-as in the right side of the fabric to the fusable side of the interfacing) stitch all the way around the shape- then you cut a small slit in the interfacing and turn it all right side out- now your shape has a finished edge and the back is fusable to place on your background.
sometimes interfacings are used to add a bit of stability to thin fabrics, or to line totes, purses- add an extra layer
it stays soft- some paper backed fusables can be quite stiff once pressed to fabrics-fusable interfacing unless it is already stiff- will stay soft/pliable.