Why would a 3-Quadrant Triac NOT be Snubberless/Alternistor/High-Commutation?
Triacs are inherently more difficult to trigger in Q-IV compared to the other quadrants, by typically about 2:1. The manufacturer may simply have decided not to characterize the standard triacs for that quadrant of operation since few experienced designers use it- it doesn't mean that they won't work if you hit them in Q-IV with double the 50mA or whatever positive gate current. 

There is a clear difference in the commutation specs between the two types- about 6:1 in the Littelfuse datasheet. 

If you refer to the older Teccor (before the Littelfuse acquisition) databook here you'll see that there are standard triacs with and without Q-IV specs, and of course all Alternistors have no Q-IV spec. 



Conclusion: Alternistors(TM) or Snubberless(TM) triacs lack Q-IV operation, but not all triacs which lack a Q-IV specification are Alternistors.