Compersion is a word created from the words “compassion” and “conversion.” It is used to describe the positive feeling a person experiences when something good happens to someone they love. It is most often used to describe being happy when your partner is in a positive relationship with someone else and is usually used in contrast to jealousy or as an antonym to it.
A metamour is a person who is your partner's partner but with whom you don't directly share a loving or sexual relationship. For example, if person A and B are dating and person B is also dating person C then A and C would be metamours to each other.
New Relationship Energy (NRE)
NRE is the term to describe the surge of emotional and sexual feelings that result from forming a new relationship. This term is useful for understanding why a person may seem to temporarily feel more intensely about a new partner than an established one. A good understanding of NRE can help in making better decisions about your own relationships and understanding the feelings of your partner when they begin dating someone new.
Generally, an open relationship refers specifically to the members' ability to have sex outside of that relationship. This terms overlaps with polyamory but does not mean the same thing. While an open relationship specifically refers to sexual freedom, polyamory also includes the freedom to develop meaningful and committed relationships. Not all poly relationships are open (e.g., a polyfidelitous group relationship) and not all open relationships are poly (e.g., a monogamous couple who practices swinging).
Polyfidelity is a term to describe a relationship between more than two people (such as a triad or quad) in which the members may have romantic and sexual relationships with each other but have agreed not to date outside of the group.
Primary, Secondary, Tertiary, etc.
These terms are most often used to describe the seriousness of a relationship in regards to involvement, commitment, and/or priority. It is not uncommon for a person to have multiple primary relationships or multiple secondary relationships, and so on. There is no exact distinction between these categories, although a general guideline would be as follows: a primary partner is like a spouse, in terms of sharing finances, living together, raising children, etc. A secondary partner can still be very serious and long-term but might have fewer of those aspects. Tertiary is more rarely used but would describe a more casual relationship. Some polyamorous people prefer not to use the terms primary, secondary, etc., since they imply an arbitrary limit on certain relationships and don't allow the freedom for each one to grow in its own way.
A quad is a relationship between four people. The relationship is not necessarily sexual in nature between all members. In fact, many quads have certain members who are never sexual with each other, although this is not always the case. A quad can even consist of two overlapping triads, where two of the members are not romantically involved with each other but are involved with the other two. Occasionally, letters are used to attempt to describe the shape of the relationships in a quad. For example, "U," "Z," and "N" are often used, although there are many quad relationships that don't easily correlate to a letter shape.
Swinging is a term used specifically to describe a couple that has given each other permission to have sexual relations with other people. Often, but not always, swingers will have specific rules preventing them from creating any emotional connections with their outside sexual partners or other rules to limit the people they can sleep with (e.g., only sleeping with approved mutual friends). Polyamory, on the other hand, is focused on creating emotional bonds and relationships, and these are not necessarily sexual at first (or at all, in some cases).
A triad is a term for a relationship between three people. This relationship is not necessarily sexual in nature between all members. Triads generally fall into two categories, described as a triangle or a "V." A triangle is a triad where all three members have a roughly equal relationship with each other sexually and romantically. A "V" is a triad where two of the members don't have a romantic or sexual relationship with each other but instead have a relationship because of their connection to the third member (who is sometimes referred to as the “hinge” or “pivot”).