Since the European theater and the Pacific theater of WW2 were largely fought by different nations, and were caused by different reasons could they be considered different conflicts that flared at the same time?

I'm not sure where you're getting the idea that the two theatres were fought largely by different nations, but British, Commonwealth (Canada, Australia, New Zealand, India,) Dutch, and Soviet forces fought in both Europe and the Pacific theatres, alongside American forces.

Gerhard Weinberg's A World at Arms: A Global History of World War II is a really good place to get an idea of just how truly global and all-encompassing the war was, and how much European and Commonwealth forces participated in the war in the Pacific.