In short, polyamory is the act of having intimate relationships with more than one person at the same time. However, polygamy exclusively describes relationships where people are married. Polyandry and polygyny are both forms of polygamy (in other words, they involve marriage too).
Are polygamous relationships legal?
United States. Polygamy is the act or condition of a person marrying another person while still being lawfully married to another spouse. It is illegal in the United States. The crime is punishable by a fine, imprisonment, or both, according to the law of the individual state and the circumstances of the offense.