the most basic and widespread variant i got to play was the one where there are 2 teams, if ur hit you sit down and if your ball is caught you sit down. balls only have these effects if they have not touched ground or wall since being thrown. if you catch a ball thrown by the enemy team someone on your team who's sitting gets to rejoin the game, probably the first to be sat
first notable variant, and one I played in my elementary school, I think might be called slapball: put a bunch of tables up to create a constrained play area with raised walls. only one ball is in play, if the ball bounces out of the play area a spectator will toss it back in. there are no teams. you may not hold the ball. you may only touch the ball with your palms, and if it touches any other part of you you're out and must leave the play area. last standing wins
then there are a few that one weird 8th grade coach tried a single time with a class he felt was well behaved, that I was just reminded of because of a video on youtube—
normal dodgeball rules apply. when you would normally be sat, instead go to the other team.
there are 2 teams: dodgers and throwers. dodgers may not throw balls, but may catch them. dodgers are expected to not hoard the balls. when a player would normally be sat, they switch teams. this variant may be played with teams arranged on opposite sides of a room, as usual, but sometimes is played with dodgers on the inside of a circle and the throwers on the outside.
as the kid smaller than everyone else with no endurance or strength, we found it really difficult to enjoy PE, so we always loved dodgeball when it came around. it's more or less the only thing you can enjoy if you're simply the kind of person who has a smaller hitbox than everyone else and you have nothing else going for you. we also loved that, though there were win conditions, they didn't ever really feel like winning mattered, we just loved dodging. we kinda miss it a lot and we're already looking into whether it'd make sense to seek out something similar as an adult, especially since we get essentially no intensive exercise nowadays.
also realized that it makes sense we're a system of touhous due to an established lifelong love of dodging, and, fuck.