An instruction pointer versus a program counter?

Question

Is there a fundamental difference between an instruction pointer and a program counter? I believe that both of them refer to the same eip / rip register, although with the studies that I have done so far, this is not very clear in my mind.

Answer 1

No, this is the same. This architecture will relate to exactly one of them (in particular, x86 and x64 use IP instead of PC).