Although bigamy and polygamy are similar in meaning, both referring to being married to more than one living person at the same time, there are differences between the two terms.
What usually differentiates bigamy from polygamy is that the spouses of the bigamist usually don’t know the other marriage exists.
Although “bi” is the prefix for two and “poly” is the prefix for many,1 laws made to prevent the practice of marrying more than one living person at a time may use either word, depending on the state.
For example, in Utah and Virginia, the term bigamy is used, and in Massachusetts, the term polygamy is used even though the law mentions only a “second husband or wife.”2 Penalties also vary by state.
The sourced articles below provide more information on bigamy and polygamy.
Footnotes: 1. grammarist.com, accessed 7/13/2018; 2. “Section 15: Polygamy,” The General Court of the Commonwealth of Massachusetts, malegislature.gov, accessed 7/13/2018