Ok, here my confusing thoughts about the matter:
A WW implies for me lots of contenders.
Simplifying:
The WW3 was West and satellites vs USSR and satellites. So IMHO it was a WW.
I t was a cold war, but it had some damn hot episodes - Korea, Vietnam, Afganistan, etc.
The WW4 it started just when the 3 ended with the dissolution of USSR. It is another kind of war, but we had two wars in Irak, another in Afganistan, and then lots of internal conflicts in Libia, Siria, Egypt, Yemen. And terrorists attacks everywhere.
Maybe it is not a proper WW like the others (that had clear contenders) but a readjustment of the balance that was broken with the end of Cold War. In any case it is a fucking nightmare.