There are some beer style guides out there that will give you the exact ranges of each style, but typically I have seen more malt, more hops and more alcohol in the double, triple, etc.
It's also a moving target. A double on the east coast may only qualify as a single on the west coast ( although they seem like they are coming more together as American vs English these days ).
I think the official delineation is based on alcohol percentage. Of course with higher alcohol, you usually need more hops and malt to balance it all out.
Seriously, though, an IPA is considered to be a somewhat stronger and hoppier version of a Pale Ale. An American IPA is an IPA, but possibly stronger, and with American (citrusy or piney, usually) hops.