Americans try to identify the "good guys" and "bad guys" in a conflict. Making that determination in modern Syria hasn't been easy. The formal government of Assad looks bad but the jihadist involvement of many anti-government rebel groups also makes them uncomfortable partners for the U.S.
I've found an RealClearWorld article about this confusion in which author Shoshana Bryen labels what's going on "The Fourth War." Her formulation identifies World Wars I and II in the normal way, labels the Cold War as War III, and interestingly, identifies "The Fourth War" as the conflict between Sunni and Shia Muslims with the U.S. having little direct role.
COTTonLINE has labeled the U.S. conflict with militant Islam as "the Long War," not a term invented here but one that describes a number of conflicts arising from the clash of western culture with strict Islam. Byren sidelines these and sees instead the Shia-Sunni conflict as being the main battle. I don't know that I agree, but her description of what's going on is certainly an interesting one, worth your time.
