The term "swag tip" is a bit puzzling. I haven't heard it before, but I'd also guess that it has something to do with the word "swage".
As Bugs pointed out, "swedge" is a variation of "swage". A swage is a forging tool that's used in pairs to make the swedge on a blade. The bottom swage is secured into the anvil and the top swage gets hammered. A swedge isn't sharp, but a false edge is.
"False edge" is an old sword term. The false edge is a sharp back edge that doesn't run the whole length of blade; hence, it's also sometimes refered to as the "short edge". It is distinguished from the "true edge", or the main edge of the blade, which stays sharp all the way to the ricasso, or shoulder, or whatever. The true edge is also called the "long edge".
"Double ground", to me at least, means that there a two primary grinds that are roughly the same width and length, so the blade shape would be symmetrical, or close to it. The stereotypical dagger blade is double ground. I don't think that double ground blades must necessarily be double edged though. "Double edged" refers to two sharp edges that run the full length of the blade.
The basic definitions would be something like this:
Swedge - Beveled area at the spine that doesn't run the whole length of the blade.
Double grind - Beveled area at the spine that does run the whole length of the blade.
False edge - Sharp back edge that doesn't run the whole length of the blade.
Double edge - Sharp back edge that does run the whole length of the blade.
There will be some grey areas though. For instance: If a knife has a bevel that runs the length of the blade, but isn't as wide as the primary grind, is that a swedge or is it double ground? An example of this would be Bob Dozier's Arkansas Toothpick.
But anyways, I sharpened about 5/8ths of an inch of the swedge on my Chinook and I thinks it's great. As for legalities, I personally haven't seen a state law that explicitly outlaws knives with two sharp edges. Some states have laws against "daggers" in some form (usually to carry concealed), but what they mean by that term is anyone's guess as it's rarely defined in the statutes.