Polygamy: The marriage of more than one spouse. (There are many forms however!)
Polyamory: This means to have more than one open relationship at a time. (Non-monogamy Poly)
Polygyny: This is where a male has more than one wife . (Sister Wives)
Polyandry: This is where a female has more than one husband. (Brother Husbands)
Polyamorous Or Group Marriage: The state of having multiple sexually or romantically committed relationships at the same time, with the consent of all partners involved.
Polyfidelity or Polyexclusivity : Involves multiple romantic relationships with sexual contact restricted to only specific partners in the group.
Poly-mono: Where one person only has sex with their partner, but the partner is allowed to have other lovers.
Triad: Usually when a couple becomes partners with a third partner they become a triad. They each have sex with each other or as a group and are usually closed.This involves equal relationships between all partners.
Ok i hope that helps. There are still disputes to what some of these words mean, but these are the general definitions from common popular sources.