How does polyamory differ from polygamy?

Bigamy is the unlawful act of knowingly having two or more wives or husbands at the same time, with the second not knowing about the first. Polygamy is the practice of having multiple wives based on religious beliefs, with all wives aware of, and agreeable to, the husband having several wives. The wives of polygamists refer to each other as "sister wives".

With polygamy, the more common practice is to have a legal marriage with the first wife, then the subsequent marriages are performed by an elder of their church instead of having a legal marriage ceremony as is done with their first marriages. This is their way of avoiding prosecution, since they know the subsequent marriages are not legal, nor are they recognized in any way by the state. So only the first wife receives any benefits as the legal spouse, with the sister wives receiving none.

In the United States only the first marriage is legally recognized. Any subsequent marriage, without obtaining a divorce, is invalid.