There is a small difference in Part 1, that being when Kaiji goes to the other room on the Espoir, he gets his passport destroyed and he's branded.
If you were referring to differences in gambles, there are a few
Part 3 has a simplified version of Mahjong called '17 Steps' or Minefield Mahjong. The manga does a decent explanation of it and it requires no knowledge on mahjong (read it long before I got into mahjong or any of FKMT's mahjong heavy manga).
Part 4 has a game that I'll only give the name for. It's called Three Asian Stepladder and doesn't involve Kaiji, he just watches. It's similar to the balancing beams in Part 1, where they're doing a physical activity.
Part 5 has a simplified version of poker that is called One Poker. You get two cards, and you both play one of the cards there. The person with the higher card wins, but if someone plays a 2 against an Ace, the 2 wins.
A machine will announce if the cards are Up or Down. A down card is 2-7, and an up card is 8-10 and all face cards.