Let's be real - I fucking hate labels. A lot of the time they just don't quite FIT what's actually going on.
But since we're throwing around terms, I wanted to give a general overview of what these terms mean. And remind you to really make your relationship what you & your partner want it to be. You don't have to label it if you don't find something that fits exactly right. Additionally, you may have a slightly different way to define these things for yourself and your relationships - that's ok, too!
Monogamy: committed to one individual. These are the societally accepted standard marriages, couples, and relationships.
Open relationship: A relationship where the individuals involved have some degree of freedom to love/sleep with people outside the relationship. Individuals may not know of every sexual encounter their partner's have. These may be couples who don't want to split up, but also may not be sexually satisfied within the relationship and have decided to allow each other to openly seek out others to fulfil those needs.
Non-monogamy: relationships with multiple people - often not disclosed to all parties; non-exclusivity/non-commitment within a relationship; dating/sleeping around
Ethical non-monogamy: relationships with multiple people in which everyone is aware of each other and in agreement of the style of relationship. Not all individuals may know everyone involved personally, but everyone knows everyone else exists. (Kind of like knowing the names of your partners' coworkers - you may not know them personally, but you know a lot about them from what they tell you.)
Polyamorous: Multiple committed relationships - often living together and having a level of domesticity; includes group marriage; often these relationships are closed to any other individuals (ie. they are non-monogamous with each other, but not with anyone else). These relationships often have a lot of non-sexual interactions - having dinner together, living together, going on dates together, etc., in addition to the sexual component.
Again - this is just an overview - feel free to discuss some of these options with your partner and come up with your own plan!
*Some of these definitions were adapted from the book The Ethical Slut, by Janet W. Hardy and Dossie Easton.