Because the CC2 doesn't require HV switching inside the charger to achieve DC charging like the Tesla Type 2 does, Generic Type 2 plugs don't DC charge. It, CCS2, reduces complexity but still allows backwards compatibility with Type 2 AC charging. CCS2 will be the plug of choice for a long time to come.
Type 2 is a 3 phase charging plug where Tesla pairs up two each of the L1,L2,L3 and neutral pins, by switching inside the charger) to provide a DC pathway. I had the charger fail just after we completed our across Australia trip and could only charge on L1 single phase, no 3 phase or DC charging would work. USA is different as they typically only have a single phase supply hence the design of the Tesla plug which uses the same two pins for AC and DC charging.