Well, yes and no.
A bigamist is someone who has two or more “legal” spouses at the same time.
Polygamy encompasses a number of different “multiple marriage ” arrangements, some of which could technically incur a charge of bigamy but the key word here is “arrangement”.
In a polygamous relationship, all of the spouses are both aware and in acceptance of the multiple partner structure. Typically, polygamists live together, either in one household or adjoining houses and share all of the parental, financial and marital responsibilities. They operate together as one unit, raising all the children together and making all the major decisions as a team.
Polygamists are often only legally married to one spouse, bringing the subsequent spouses into the fold with a private ceremony . Others will marry and divorce each of the spouses so that bigamy charges cannot be brought.
A bigamist on the other hand is typically someone who has entered into a multiple marriage arrangement without the other spouses knowing that the arrangement exists.
In this case, the bigamist would maintain more than one household and each spouse is completely unaware of the other relationships.
Both of these types of relationships meet the technical definition of adultery, but adultery isn’t just limited to other marriages. Adultery also applies to extra-marital affairs, even if its just a one-time occurrence.