What's the difference between 3 and 4 quadrant triacs?

NXP has a good explanation as to what the differences between 3-quadrant and 4-quadrant triacs are.

Summary: a 3-quadrant triac cannot be turned on in the fourth quadrant (T2 negative, G positive) which is beneficial when dealing with inductive loads - ringing caused by sudden turn-off could potentially turn on a 4-quadrant triac, necessitating snubbers and other protection means to prevent spurious conduction.

3-Q Triacs don't operate in 4th quadrant i.e positive gate current and negative load current. Please see the link I ve shared http://en.wikipedia.org/wiki/File:TRIAC_Equivalent_Circuit.png. You will get an insight of the working of a TRIAC