+1 Art, Greg, and some others.
Fastpacking to me requires that you:
a) carry what you need for camping, eating, hygiene, etc..
b) can go for multiple days up until the food runs out
c) you are moving as fast as you can.
I just hiked into the JMT through Lyell Canyon with the family carrying extra food. Two days later we were 15 miles in at Marie Lakes Jct - slow hiking. I then gave them the food and took back a bunch of stuff they realized they didn't want to carry to Whitney. With a now 38 LB pack, I fastpacked back to the car in 1/3 the trail time it took to get in.
I fastpack to press my limits and see what wrings out. I discover things more subtle than mere pack weight. Obviously UL speeds things up, but the energy output is the same. I learn about the various gaits I employ, how to navigate staircases at speed, how quickly can I run the pitstops.
Beyond technique, I learn about my mental issues that impede speed - losing discipline in refueling, electrolytes, hydration; counting or not counting the time to take a leak (not counting means I can get a longer rest for free); succumbing to the 'countdown' near the end that seems to stretch for eternity and saps willpower.
So to me fastpacking is a primarily athletic endeavour in the context of backpacking and backcountry. To distinguish it from trail running, I would say it has to be unsupported and at least be capable in theory of stretching over many days, limited only by food and fuel carried. Equipment choices, as for any athletic endeavour, can affect your absolute times, but not whether you are engaged in the sport or not.