Yes, the non-monagamous set have their own set of vocabulary to describe what the do and how they do it. It isn’t exact, and people often have different definitions on the same word.
Cheating: Having sexual or emotional relationships outside your relationship without the knowledge/consent of your partner/s.
Monogamy/Monogamous: Being only with one person, both sexually and emotionally. Includes serial monogamy. Technically, it should mean just one marriage if you look at the roots mono-one gamy-marriage, but the word has obviously branched out to cover relationships outside of marriage.
Non-monogamy/Non-monogamous: Any situation where you are emotionally or physically with more than one person. Cheating, open, polyamorous, polygamous, swinging.
Open: This is my favorite word out of this set because it is so vague and it doesn’t connotate raunchy sex like the word swinger does. I take open to mean a person is in a relationship and is open to others in some way. This could mean they are open for a relationship, sex, both, or something in between all of those. When I hear the term open I assume open to sex and possibly open to emotional connection.
Polyamory/polyamorous: Literally more than one love. I use this term to describe people that are open to the idea of emotional connections with more than one partner. So you could be single and polyamorous.
Polygamy: Married to more than one person. The word is gender neutral, but usually polygamy is referring to a man with multiple wives.
Serial Monogamy: Multiple monogamous long term romances or marriages.
Swinger: A person that engages in an open sexual lifestyle with others and has one or more partners. This term is very sexually oriented. Covers all sorts of activity.
Walk-in Closet: A term I use to signify the metaphorical closet that many non-monogamous people hide in either by choice or out of fear. I like to imagine I came up with it myself, but in reality it isn’t a large intellectual leap from the closet that GBLT people hid in to a bigger closet for the multi-partnered to hide in, so I imagine someone else has come up with this term as well.