Polyamory and nonmonogamy are not interchangeable terms. You can technically have a monogamous polyamorous relationship. What’s the difference?
Monogamy is sexual exclusivity to one person, or a few people. You’re monogamous with your boyfriend when you’re only fucking him and he’s only fucking you.
Nonmonogamy recognizes the problems with monogamy (more on that later) and defines relationships in which sexual exclusivity varies. Nonmonogamous couples may occasionally play with a third, or have separate trysts on the side, or have dominant/submissive relationships with other people, or play with others only when they’re apart, or may establish certain freedoms on certain occasions. (For example, many gay couples give each other permission to play freely with whomever they want on Pride weekend.)
Polyamory is simply the practice of loving various people at the same time. The difference between these two terms is that “non-monogamy” implicitly defines a “primary” two-person relationship with various secondary and tertiary partners on the side. In contrast, polyamory rejects a central two-person pairing as the “main” one, and sees all relationships as different, equal, and important, existing in tandem with each other. If nonmonogamy is a web with strands spread out from the center, polyamory is a series of strings laid together, running parallel.
“Nonmonogamy” is generally talking about sexual exclusivity — the “focus” of the word is sex. Polyamory (composed of the Greek poly meaning "many, several" and the Latin amor, “love”) defines many loves, many relationships. Its “focus” is affection for multiple people, regardless of sex. I am a non-monogamous polyamorous gay man.