Lou,
From what I understand, a jigsaw is handheld and the blade is only attached to the saw at the butt end. You push the saw into the wood to use it. (It's close to a mechanized version of a regular hand saw.)
A scroll saw has a thin blade that's attached at both ends to a larger stand; it's a table saw. The blade moves up and down, and you push the wood into the blade. The thin blade and the fact that you're feeding the wood into a fixed blade allows you to rotate the wood around and cut all kinds of shapes with a lot of control.
Not sure on the Dremel thing; I'm inclined to say that if I want a saw, I might as well get a saw rather than trying to make my poor Dremel carry the load. :)
Josh