Eh, it'll be easier to point to the differences between polygamy and polyamory, simply because the latter doesn't really have a set definition other than "many loves," which is ridiculously open to interpretation at times:
1) Religious Based
Polygamy, while technically meaning "Many Spouses" has a very traditional historical connection to certain religious followings. In the US, the most common is fundamental Mormonism. In the case of Mormonism, especially in these fundamental sects, it's an expectation to reach spiritual gain in the afterlife for a man to have at least 3 wives in the physical realm. It's also referred to as Celestial Marriage. And it could also be technically called Polygyny (or multiple-women). Despite its technical meaning, Polygamy has gained a societal description to refer to group marriages with dominant male and multiple wives [like harems]. I could go on and on about the history behind this and the reasons... and it's quite fascinating from a sociological position. But I won't bore you with it... google "polygamy" and "mormon" and you'll find plenty. But keep in mind, polygamy is strongly tied to religious expectations.
Polyamory itself has no religious connections. Sure, the people who practice it may come from various religious backgrounds, but the pursuit of multiple relationships has no specific spiritual basis or goal. People practice it for their own reasons - which may widely vary. It's all personal choice (or should be, in my opinion). But LOVE is usually a strong reason for polyamory... and the freedom to love and pursue relationships with as many people as you want. Not for a love of a god figure, or for entry into special status in the afterlife.
2) Male dominated vs. egalitarian
In traditional polygamy, it is extremely male dominated. While "Many Spouses" is non-gender specific, the term polygamy most often refers to a Male dominated relationship with multiple submissive females (and not in a BDSM sense). Oftentimes, the women have little say in when other wives are brought into the family, and the connections between the wives vary from not knowing each other to co-habitating and raising families together. One extreme is the Kingston family shown on the documentary, where the women are forced into marriage by age 16 (usually to an uncle or such), and expected to produce a child every year. Each wife usually has their own house, and raises the kids on her own. But that's an extreme. In the "normal" Mormon polygamist family - there's a little more choice on the part of the women coming into the family, and the existing wives having some say in the new bride. But it's still very male-dominated. None of the women are allowed other partners. And the male makes most decisions.
Polyamory can be described as egalitarian. Sure, a polyamorous household may be one man and multiple females - but it's by the choice of each involved, not because of some spiritual expectation. And the man is rarely dominant in these situations. In polyamory, women and men have equal status and choice in the matter of relationships. Polyamory celebrates individuality and choice. It's not uncommon at all for a woman to have multiple boyfriends (and girlfriends), for a guy to have boyfriends and girlfriends, etc. For a couple to date another couple, etc. Sure, when you combine BDSM with Polyamory, you may get a dominate figure with multiple submissives... but this is far from the "norm" in the polyamory I've seen. And that dominant figure can just as easily be a female as it can a male.
3) Multiple Spouses vs Multiple Loves
Polygamy is definitely about plural marriage, after all, the term does mean Multiple Spouses. If you take out the historical and religious connotations - this would be the biggest difference between polyamory and polygamy. Polygamist do not date just to date... they bring in candidates for marriage. And sometimes, love of the actual person is a component of the marriage... but it's certainly not the purpose.
In polyamory, marriage is rarely the goal. Sure, you'll find groups that called themselves a group marriage. And while they could technically use the term "polygamy" to describe their lifestyle... few do, for the connotations described above. (Most closed group marriages actually use the word "polyfidelity" to describe themselves.) And you'll even find group marriages in polyamory that are not closed - the individuals still can date others, even without the intent of bringing in new partners into the marriage.
Polyamory simply means "Many Loves". It does not imply that people are looking to marry multiple people. Those loves may be explored in a variety of relationship styles - from dating, to living together, to raising kids together. But there is no "ideal" of marriage in polyamory.