Kabaddi deserves a mention for the first category. Zero equipment used, you play with your body. Played as a team and teammates are absolutely indispensable for every maneuver or play. Alternating roles of teams, and your team's immediate objective (avoid contact or make contact) changes instantly. As a game of stamina there is an internal struggle as well as an external one.

For the second category I don't think anything beats American football. Hyper commercialized, direct physical confrontation, star status of a few players with most of the rest playing subordinate roles, really destructive to the body and it almost celebrates this. The odd thing here is that rugby doesn't even really fit the category, with its continuous gameplay, less dangerous contact, and plays that are a string of everyone's actions as equals.