If you drive the ball 300 yards, 400 is a short par four. If you drive the ball 200 yards, it's not.
If a hole is downhill, playing downwind and has a firm fairway, I might bounce one on at 350, so I suspect that 350 is the longest to which I would grant "Short Par 4" status.
The subsequent notation is typical set of tees. If the back are 390 but the middies where I play are 350, it's a short par four for my list.
Some might say "driveable in all circumstances." If that's the case, my distance designation must change.
I agree that we should have a definition, albeit perhaps only a personal one. I'll be back with my 350-And-Under collection later.