You're right
The only difference I can see, is that most wars post the Reformation have not been fought in order to spread christianization per se, unless you include the atrocities commited by the Spaniards against native Indian populations. Purists might say that Catholicism was responsible for the crusades, the inquisition, the slaughter of native Americans in South and Central America, etc. , not protestanism.
Curiously, the very central point of christianity is that Jesus came to redeem a hopelessly fallen human race, that is and was at odds with God and each other, and thus producing the constant battles. Hence the very idea of Jesus, is to reconcile man to God and escape that within our nature that causes us the drive to be at war.
I believe there are times when one group of people commiting evils against another group is at fault, and then at some other time it will be some other group. No matter what part of the planet we look at, there is always a place and time when we can point fingers, there is never a time when everyone is guilt free. From that standpoint, all are at fault, and yet in individual instances in history, some are much more at fault than others.
The causes vary, the motives are different, the perpetrators and victims switch places, but the underlying human condition is always the same.