They have different descriptions so I'm guessing they're not synonyms for each other. The descriptions don't seem to clearly make a difference between the two, however. Is one supposed to be used for a specific instance of war, and the other for questions about general warfare/tactics/strategy?
The way I understood it, war is for questions on specific wars (perhaps ones that aren't covered by existing tags like ww1?), e.g. What would've been the outcome of the Yom Kippur War had the UN not intervened? In contrast, warfare would be for the history of waging wars in general, e.g. questions like When was the first airborne combat drop?
As is typical with such tags, in practice they get mixed around a lot. I think that in this case though there's a non-trivial difference and on the whole I think people (or editors) are tagging them differently.