My relatively uninformed estimation:
Polyamory encompasses a broad range of relationship dynamics, ranging from extremes of relationship anarchy to serial monogamy, but mainly it is about forms of loving relationships with multiple partners, not necessarily all sexual, and not necessarily all directly connected to each other. It seems to be often motivated by secular, or at least non-religious thought. Very often the relationships are idealized as being egalitarian and non-possessive. Even attachment may be placed lower on the value scale: Solo-poly generally does not seek shared housing, finances or possessions with intimate partners, preferring to maintain more independence.
Polygamy is mostly centered around one spouse, a man with multiple wives or more uncommonly vice-versa. It might be thought of as a special case of polyamory, but it is typically possessive, and associated with certain religious or cultural traditions. There may also be an apparently one-sided power dynamic, sharing of resources, and greater economic dependency on the part of the wives.
Note that a marriage between multiple people is still bigamy, which is illegal.