dcr was pretty close: a more exact explanation from my EMS colleagues:
Class 3: BLS Non-emergency
Class 2: BLS Emergency (around my area, almost always with a medic anyway)
Class 1: ALS Emergency
Odd, no ALS non-emergency
Also, on fire calls, The 1-A refers to the box size, i.e. 1 Alarm, 2-A is 2 Alarms, etc.