How is polyamory different from polygamy?
Polygamy is a legal-marriage configuration in which one person is married to multiple spouses. Polyamory is a relationship-orientation that involves multiple loving partnerships, with marriage being optional. They are different categories that overlap in some traditional polygynous contexts but are otherwise distinct.
Polygamy is specifically about legal marriage. It describes a configuration in which one person is married to multiple spouses simultaneously — most often polygyny (one husband, multiple wives), less often polyandry (one wife, multiple husbands). Polygamy as practised in cultural and religious contexts (some Mormon-tradition communities, some Islamic contexts, some traditional cultures globally) is typically hierarchical, often patriarchal, often heterosexual, and tied to specific religious or cultural prescriptions about marriage.
Polyamory is about loving multiple partners with everyone's consent, regardless of marriage status. Polyamorous configurations may include legal marriage between some partners, but the polyamorous part is not the marriage; it is the multiple-loving-partnerships part. Polyamory is non-hierarchical by default (or hierarchical only by explicit choice), often egalitarian, frequently queer, and not tied to any particular religious or cultural tradition.
Where the terms overlap. Some polygynous contexts could be described as both polygamous and polyamorous if the participants are operating with full consent and informed agency. In practice, most cultural polygyny does not meet the consent threshold polyamory expects (women often born into the structure, marrying in their teens, without practical alternatives). The reverse — a polyamorous family with legal marriage between three of its members — does not exist in US law and would be polyamorous-but-not-polygamous if it did.
Legality. Polyamory is legal everywhere in the United States as a relationship practice; polygamy is illegal everywhere as a legal-marriage configuration. The distinction frequently gets blurred in popular discussion. The bright line: legally marrying a second spouse while a first marriage is in force is bigamy and is criminal. Having multiple loving relationships, with explicit consent from all, while legally married to only one of them at most, is polyamory and is unrestricted.