It's not the same thing. One way to solve this is when you cut out the fusible for the shape, cut out the center of it, leaving 1/4" or so to the inside of the drawn line - kind of like a frame. The edges will be fused, but the center won't be. You could then carefully cut the background fabric away leaving just the applique.
If you scroll down on this link, you will see a picture of what I am trying to describe.
http://www.connectingthreads.com/tut...Prep__D47.html