The "combat as war" crew feel that fighting should only be a life-or-death, dramatic measure of last resort, and that's how it should be represented in play. They see the "combat as sport" crew as lacking a true understanding of stakes and narrative tension.
The "combat as sport" crew feel that fighting should be an opportunity for characters to display their skill and bravado, and do cool things, and that's how it should be represented in play. They see the "combat as war" crew as lacking a true understanding that this is a game and escapist fantasy.