I'm not sure how much more clear warfighter could be. "One who fights wars."

Service member is extremely vague. "A member of a service."

Growing up, "the service" was synonymous with "the military" among my grandparents who, y'know, fought in WWII

The world wars were an unusual period. When I grew up, "veteran" usually meant an old man. Most men in my grandparents' generation had seen combat.

Except for extreme periods in history (that I hope we can avoid), most service members don't end up directly participating in a war.