Well... It's a relatively new term being applied to a lifestyle choice that has been available and in at least somewhat common use for at least a couple thousand years. It's distinct from "open relationship" and "swinging" as I distinguished above. So while the term is new(ish), the distinction has existed for a long, long time.
As many as there are poly-families. I think it's fair to say that there are two general ways to come at it: either you have a primary relationship, and everything else is secondary, or every relationship you have is equal. Inside those two general approaches, there are an infinite number of possible configurations.
Right now I'm not in a relationship with anyone other than my wife, but I'm casually seeing a couple other women, and so is she. I'm in the "I have a primary partner, everything else is secondary" camp. That doesn't mean that secondary is unimportant, just that without my primary partner's knowledge and approval, nothing secondary is ever going to happen.
I know of a woman (who happens to be in the "all my relationships are equal" camp) who is in a relationship with a married man, whose wife has two other lovers. That married man has three grown children, one of whom is married and has another lover. The beauty of polyamory is that you can say what works for you, want you want and don't want, and--while that puts a certain responsibility on you to create relationships that work inside of that--you're free to do and have whatever you want to do and have.
I strongly recommend the Polyamory Weekly podcast if you're curious about Poly.
http://www.polyweekly.com. As (I guess!) TFP's honorary poly spokesperson, I'm happy to answer any other questions you might have.
That certainly hasn't been my experience! Being poly has stretched me so much as a person that I hardly recognize myself. It has had me confront my whole bag of tricks that I bring to relationships.
That hasn't always been pretty, but the results have been well worth my effort. I can no longer pull my petty jealousy shit without seeing it coming and having the opportunity to head it off at the pass. I've become a
vastly better husband out of being polyamorous. I now know that sometimes my partners need to know that they're cherished and valued, and I'm way past my tendency to neglect that need or play that down.