Polyamory: Multiple Partners in a relationship. This means multiple people in a single relationship, not two people in a relationship with other partners. People in a poly relationship make all the same decisions people in regular monogamous relationships do, as a group. I want to break this one down Poly means many, amory means loves. The basic understanding of this is exactly that many loves. A group of people who all love each other, even if they are not all having sex together.
Polygamy: Multiple spouses, they don't have to like one another at all.
Polygyny/Polyandry: A man with multiple wives/ woman with multiple husbands. Gender classification of the terms.
Polytheism: Multiple gods, this doesn't mean church sanctioned polygamy.
Open Relationship: This is a when you have a primary relationship, and a partner on the side you may or may not have strong feelings for, and your primary partner doesn't either. Basically this means your primary partner doesn't care if you sleep with other people. That is the basic term.
Metamore: Your partners other partner who you love and care for but don't sleep with. Your partners other partner isn't your metamore if you wish they were dead.
Swingers: A couple that sometimes has sex with other couples, often called wife swapping. You don't have to be in relationships with these other couples.
I'll add to these as time goes on, please feel free to disagree with me, but I feel that it's important that people really understand the difference on these things, for political reasons.