Polygamy

Polygamy
       ("poly-") many
       ("-gamy") marriages ---i.e., opposite-gendered marriage-mates.

In a technical sense, polygamy is a neutral term which can refer to
either polygyny (one man, many women)
or polyandry (one woman, many men).
(It never refers to polyamory or group marriage.)

In a cultural sense, however, it is commonplace to refer to polygyny simply as polygamy, even when a person's own beliefs would not accept polyandry (such as Christian Polygamists who consider polyandry as Biblically defined adultery).

In fact, few people are actually familiar with the technical term of "polygyny". Thus, "polygamy" has become a colloquial expression meaning "polygyny" exclusively.

For these reasons, when most people refer to polygamy, they are most usually only referring to polygyny, a man with more than one wife.

By definition, though, polygamy is only one of two things: polygyny or polyandry.

In polygyny, the husband is identified as the polygamist, while his wives are not. The "gyny" part of the word, polygyny, refers exclusively to "women" in therefore defining the meaning that the polygamist husband is only married to women, females, wives. He is polygamous to them, while they are each individually monogamous to him. The wives are neither married to each other nor to anyone else.

The same principle applies to polyandry. In this case, the wife is identified as the polygamist, while her husbands are not. The "andry" part of the word, polyandry, refers exclusively to "men" in therefore defining the meaning that the polygamist wife is only married to men, males, husbands. She is polygamous to them, while they are each individually monogamous to her. The husbands are neither married to each other nor to anyone else.

This shows that polygyny refers to a polygamous husband with his wives who are monogamous toward him. In that same way, polyandry refers to a polygamous wife with her husbands who are monogamous toward her.

Because polygamy can only be polygyny (one man, many women) or polyandry (one woman, many men), polygamy does not refer to or involve "same sex marriage," polyamory, or group marriage.