Trying to put it simply and in plain English (yes i know it's not word for word so don't jump on me too hard).
Performance Categories A and B refer to older pre JAA legislation that may still be relevant in some cases.
The more commonly used criteria are the JAA performance Classes One, Two and Three.
Performance classes one and two apply to only twin engine helicopters whilst perf' class three may apply to twin or single engine helicopters.
If operating in performance class one, the helicopter must be operated in such a way as to ensure that, in the event of the failure of an engine, the helicopter can either continue with flight or carry out a safe landing (note landing not forced landing). (this is loosely aligned with the old Cat' A)
PC 2 accepts that rather than carrying out a landing, a forced landing may be necessary.
PC3 accepts that a forced landing will be necessary (obvious in the case of a single engine helicopter). (Approximate to old Cat' B)
Definitions (roughly).
"Landing": Basically, the helicopter will return to the ground on a suitable surface and land without any damage (although it's generally accepted that some damage to brakes and tyres is allowed for wheeled helicopters). An example of such an area would be a runway or a clear flat grass area with no obstructions.
"Forced Landing": the helicopter may land in an area less well suited and may sustain some damage but there must be the reasonable expectation that there will be no serious injuries to the occupants. There must be no damage to persons or property on the ground. An example of this might be ditching on water or running through a hedge or other obstacle that would damage the helicopter but not affect the occupants. A forced landing is definitely not a "crash" it must be fully controlled with consideration given to the area being used.
As for what an operator is required to operate to:
It very much depends... In the case of UK onshore Public transport i believe that an operator may operate down to PC3 (it will depend on what they have specified in their Operations Manuals) although there will be circumstances when PC 1 is required - for example operating in a congested area like a town or city or in a "hostile environment" where a due to terrain or location a safe forced landing cannot be made. Outside of areas where the CAA insist on PC1 for the above reasons it will be up to the customer to check / specify the performance class available / required.
As for non public transport - well they're allowed to "crash" but they must do it without damage to persons or property on the ground.
Hope that's useful - i now wait to be picked to bits.
Cheers
Barny