The "culture war" is about who's going to get control of the government for their own agenda. The political war is about keeping the goverment out of the culture war.
You have it exactly backwards. The political war is about which side will control the government, the left or the right. The culture war is about whether or not the culture itself, including the government will be forced to accept deviant immorality in the guise of "tolerant" leftist social values.