Airking,
Your post implies that those two things are one and the same with a different name for ICAO and JAA.
However, this is not the case. As describe in JAR-OPS 1 subpart F, an operator shall ensure that aircraft in a specific performance class (A,B, or C as in your post) are operated in accordance to the specific subparts describing those performance classes (subparts G, H and I). In those subparts specific performance requirements can be found such as: screen height, climb gradients, T/O and landing distances, minimum height and more.
In subpart E, JAR also makes a division in Aircraft Category, based on Vat, this is the same as with ICAO as in your post. Those categories are used when determining the MDH/DH and minimum RVR for an approach.
So, any aircraft will be placed in a performance class (A,B,C) and in a Aircraft Category (A,B,C,D,E). And yes, both are used with respect to performance, but in a different way. Indeed a bit confusing.