*sigh*
Polyamory is having intimate relationships with more than one person - typically sexual but not always the case. Always fully consensual and both partners must agree. Otherwise it's just cheating. A polyamorous person can be married and still date other people, but do not marry one another.
Polygamy, however, is the act of being married to several different people. This term is exclusively for marriages.
In polyamory, both partners are allowed to have another/multiple other lovers. In polygamy, only one partner has multiple lovers, and the other is exclusively in a relationship with them.
Polyamory is open relationships with communication. Polygamy is married consensual cheating.
So in short there is, in fact, a massive difference.