Tottigol is 100% correct in his quoted definitions of Cat A and B. Where some people get confused is when they mix Cat and Class.
Cat A as tottigol points out, covers other aspects of certification ( dual hyd, fuel systems, etc.) as well as performance, whereas CLASS 1 is performance only. Cat A performance and Class 1 are basically the same for arguments sake.
Now Cat B and Class 2 are two different things. Class 2 definitely does not include single engine helicopters (class3) and has a defined performance definition.
When people are discussing performance it is far more accurate to use the Class definition than the Cat