Personally, I've always seen an IPA as more bitter than a pale ale (but not necessarily more "hoppy" - that's subjective, I guess).
Now, in reality, a lot of beers don't always follow these conventions, but to say what the difference between an APA (American Pale Ale) and an American IPA, I find that IPAs are usually higher in alcohol, higher in bitterness, and dryer.
Like, I made an APA a few months ago that no one could ever consider an IPA by any definition (although I'm sure a ton of people would drink it and say "Hey, this is an IPA"), but fit perfectly into the APA category. It was 5% ABV, had about 35 IBUs, and had very citrusy hoppy aroma and taste from citrusy American hops (such as Cascade, Galaxy, Citra, and so on). In comparison, the last IPA I made was 6% ABV and 60 IBUs. The last double IPA I made was 7.5% ABV and 90 IBUs. The last triple IPA I made was 9.9% ABV and 100 IBUs (but way more bitter and hoppy than the double IPA I made before it).
But, yeah, there is a ton of overlap, especially on the lower end of IPAs and the upper end of APAs (likewise, there's some overlap on the British styles too with British pale ales and IPAs).