Stag and vixen: Nothing intense. No domination nor humiliation. Just a man that enjoys watching his wife getting fucked and a wife getting fucked.

Slave couple: The bull is the ultimate authority when around and the couple bows before his dominance.

Cuckoldress couple: A female-led relationship. The wife is dominant to her cuck and sometimes the bull, too.

Friend couple: The bulls are just friends with benefits. The couple hangs out with and considers this bull a friend, even as he fucks the wife.

Boyfriend couple: More than a friend with benefits. The wife and bull go out on romantic dates and love is not uncommon. You also say polyamory.

Slut couple: The wife regularly gets new men and has one night stands.

Bi couple: Both the cuck and wife get fucked by there bull.

Cheating wife couple: The wife if fucking dudes against her cucks wishes or behind his back. Very toxic.

Other couple: Any dynamic I failed to list.