They can't be identical in physical location, or there wouldn't be separate particles to interact. But having established they are separate particles, the only thing relevant to their physical interaction is their physical properties, yes (although we do speak of a particle's or object's world lineWP, as relevant to distinguishing each particle before and after).
If two of the same kind of particle interact and then separate, it's not meaningful to ask which particle was which prior to the interaction. From a quantum physics point of view, these identical objects aren't just conceptually indistinguishable; they're actually physically interchangeable. Their "world lines" intersect, then which is which becomes a meaningless question.