An open relationship is a type of relationship for those who have more than one sexual or romantic partner at a time. This is an arrangement where the two parties agree to be non-monogamous or non-exclusive. If both or one of the partners engages in sexual or romantic activities that are not within the relationship, the agreement aspect of the arrangement serves as the key.
When the two partners don’t agree to a marriage or open relationship, and both or one still engages in several partnerships, this is already called an NCNM or nonconsensual, non-monogamous relationship. An open relationship is also called consensual non-monogamy. The two parties agree for the relationship to be non-monogamous. The terms polyamory, polyamorous relationship, and non-monogamy also refer to open relationships.
Polygamy pertains to having several spouses simultaneously. It is not legal in the United States. When a marriage is non-monogamous, this may be referred to as an open marriage.