When does an air hammer become a rivet gun anyway? When they get down to 1x and 2x maybe? 3x and 4x an air hammer?
Not really. You can still get a 1x rivet gun, but at that size, I know them as a buzz gun (take a smaller diameter rivet snap, and only any use for small rivets in awkward places. A 2x Rivet gun is only really any good for 3/32 or 1/8th rivets, where as a 3x is good for most size rivets, but will struggle on 3/16 steel or 1/4 ally rivets. The 'feel' and operation of a rivet gun is important, and you can also adjust the air flow on some to make them more usable on smaller rivets. Air guns, in my experience, have no 'feel' and are either 'on or off' I would never try to put a rivet down with an air hammer, and expect it to be pretty.
I guess the main difference, is the quality. The Air hammer is very rough, and agricultural in its performance. I purchased an air hammer in England a few years back, and paid about £25 ($40) for it, where as my recent CP 3X rivet gun, cost me around £100 ($160)
The best air tools in the world, in my opinion and in no specific order, are Desoutter (Now a part of CP I believe) Ingersoll Rand and Atlas copco. Snap -on/blue point air tools are not up to their standard in my experience.