What's the diff between marathon and tournament? Their own scoreboard FAQ doesn't say.
"Twin Galaxies Tournament Settings" AKA "TGTS" is a variant of play that uses rules for more difficult dip switch settings and/or self-imposed player restrictions to prevent the game from being "marathoned". This isn't really very black and white and varies from game to game. It most generally applies to the classic arcade titles where a lot of lives can be accumulated and it becomes that the difference between the top scores on these titles has little to do with a difference in skill, but rather a difference in physical endurance.
So they divided the record attempts into two categories for these types of games, "marathon" and "TGTS". There is an old stickied thread about defining "marathon" games
here.
There are a lot more relevant threads on their forums but their search function isn't so great and I don't know where they are off the top of my head.
A good example of "marathon" vs. "TGTS" can be seen by looking at the rules for Galaga:
Under "marathon settings":
3 Lives
Extra Ship @ 30k, 70k and every 70k thereafter.
Difficulty: Rank D
Special Rules: Useage of the trick to cause enemies to stop firing is banned. It has been deemed permissible for a player to intentionally play on the player 2 side so as to allow the millions-digit to show up in the final score.
Under TGTS:
5 Lives
Extra Ships: None
Difficulty: Rank D
Special Rules: Attempts for this variation may be done on Marathon Settings, but once you've lost your 4th Life, you may not allow your ship to be captured or your Tournament Score attempt ends immediately. Useage of the trick to cause enemies to stop firing is banned. It has been deemed permissible for a player to intentionally play on the player 2 side so as to allow the millions-digit to show up in the final score.
So in the case of Galaga, under TGTS, you may not allow your ship to be captured after you have lost your 4th life, nor do you get any extra lives, which really puts a damper on things:
Galaga record [marathon] = 15,999,990
Galaga record [TGTS] = 1,557,580