2 or 4 Quadrant Operation of AC Drive

We don't really use that term commonly for AC drives (despite that Wiki article). The "quadrant" concept was adopted for DC controls because making a DC motor brake (quadrant 2) or turn in the opposite direction (quadrant 3) means adding a lot more capability to a DC drive and thus the cost of the drive goes up. So if you did not discuss it clearly up front, you may end up not getting that capability on a less expensive drive, or paying extra for capabilities you don't need.

But on an AC drive, these ability are essentially inherent in the design that makes it a VFD in the first place. So reversing the motor direction (quadrant 3) is not really worth discussing, you get that capability if you want it or not. And Braking (quadrants 2 and 4) is optional regardless of direction. So although a DC drive can be 1 quadrant, or 2 quadrant (meaning 1 and 2), or 4 quadrant (meaning adding reversibility to get 3 and 4), an AC drive is always 2 quadrant (but meaning 1 and 3) and can be easily field modified to be 4 quadrant by adding a braking module (for 2 and 4). It just gets too confusing to use that terminology. The only choice in AC drives in this regard is adding braking or not.