They both pretty much mean the same thing: how war is conducted rather than specific wars. Should we synonymize them?
I do not see warfare and military as the same thing at all. War and warfare may make sense in merging, but definitely not war and military. The distinction I would make is that war or warfare is the engagement of opposing forces, while military is more specific to those who are doing the engaging. War would have more to do with battles or consequences, while military would have more to do with troops and their use.
To me the acid test for separate tags should be that they are typically used separately.
Admittedly, if you do it the other way, a large proportion (about 20%) of the warfare tagged questions do also seem to be tagged military. So basically what we have here is a situation where one tag is a near subset of another.