Interesting, I never played those formats. We usually play 4 different formats:
1) Teams get paired beforehand, on players choice. Players without partners get paired randomly. This are usually how ranked tournaments work. This can be either in play-off format or round-robin + play-offs (with or without groups).
2) teams get paired based on rankings to make balanced teams. In this one you don’t split teams during the tournament. This one is popular when there’s big gap between skills.
3) each game teams get paired based on previous score by the algorithm, whatever that means , but I noticed that if I lose I get paired with a lower ranked player, opposite when winning. The winner is who wins the most matches, total games is tie breaker. (I think this is your Americano and Mexicano format, we just use a app that makes the pairing, you just have 2 different ways of pairing teams after games)
4) the most popular where I have played: “ladder”.
Initially, You get paired randomly or by ranking, then You split on every game, you go up or down to the next court. Depending on if you lose or win. There’s a top court and bottom court.