In Chemin de Fer, players take turns acting as the banker and have the option to draw or stand. The other players then bet against the banker's hand. In Punto Banco, which is more commonly played in casinos, there is no rotating banker role, and players can only bet on their own hand (punto) or the dealer's hand (banco). Additionally, in Punto Banco, the casino always acts as the banker and follows specific rules for drawing additional cards based on predetermined criteria.