What’s the difference between Polyamory and Polygamy?

I was recently asked this question. As I write about loving polyamorous relationships in my novels, I want to be explicitly clear:

MY NOVELS CONTAIN ONLY LOVING RELATIONSHIPS. THERE IS NO COERCION OR ABUSE. AND THERE IS ALWAYS A HAPPILY EVER AFTER.

Note:
If a polygamous relationship involves consent, honesty, and equal autonomy among all partners, without fraud, abuse, or coercion, it can share many characteristics with polyamory. In such cases, the main difference becomes primarily legal and cultural rather than relational.