Swinging is what a lot of people think of when you say you're
dating more than one person at once. It refers to couples who engage in
recreational sex with others, usually only in specific settings (for
example, at parties) and/or only when both partners are present. Generally
there is no romantic involvement or long-term commitment with people not
in the primary relationship. People argue a lot about whether or not
swinging is a form of polyamory. It challenges the assumption that sexual
fidelity is a requirement for romantic relationships; but it does not
challenge the assumption that romantic love can exist only between
two people.
Polyfidelity describes a relationship in which a group of three or
more people have no sexual and/or romantic relationships outside the
group. To my mind it's sort of the opposite of swinging: it is built
around the idea that romantic love can exist between several people, but
exclusivity is considered important to the relationship.
Open marriages/ relationships are generally between two people who
have agreed that outside relationships can exist. Swingers could be placed
in this category, as can people who consider their spouse/partner to be
their "primary" but also have "secondaries" who play
an important role in their lives. Not to mention people who are devoted to
their main sweetie but sleep with their friends sometimes. (Did I mention
yet that polyamory is complicated?)
Open group relationships/ marriages also exist. Obviously, as with
couples, each group negotiates its own terms for outside relationships,
for example whether members can have only romantic relationships, only
sexual relationships, or are not restricted; whether partners have
"veto power" over their partners' choices, and so on. (Jeez,
this makes it sound like a club, doesn't it?)
Another important distinction in poly relationships is between
"V" and group relationship styles. In
"V" situations, one person will have two or more lovers who are
not involved with each other. For example, say Dawn is
involved with both Julian and Charis. Julian and Charis know about
each other - otherwise it would be cheating, not polyamory - and are
probably at least on friendly terms, but aren't involved with each other.
Charis may also be involved with her yoga instructor, and Dawn and Julian
both know about that too. (Note: you can probably tell from this example
that V relationships often look more like X's, Y's, Z's, or even W's.)
(Another Note: most "love triangles" are actually V's - mostly the people
who call them triangles are heterosexual and so are unable to have actual
triangles. I guess "love V" sounds kind of funny though.) Now, a group relationship style would be if Julian and Charis
suddenly changed their minds about each other and fell deeply in love, so
that all three of them were involved with each other.
Another category (it never ends, does it?) is what's called an intimate
network. It's kind of a vague term, which mostly refers to large
circles of friends, most of whom have some kind of romantic and/or sexual
involvement with each other, without necessarily classifying each other as
primaries, secondaries, and the like. It kind of overlaps with all of the
above.
Each relationship style has its own complexities. (I was going to write
"its own complexity", but I can't think of any relationship
style that has just one.) Complications rise exponentially with the number
of people involved, and are therefore kind of a given in polyamory. Also,
even your lovers who are not involved with each other still have some kind
of dynamic together, whether it be friendly or uncomfortable (ideally the
former). (Incidentally, this is the reason that "love triangles" got
called that in the first place)