I wouldn't say your situation is unusual -- you're in a poly-fidelitous triad. While it's not what many in the poly community end up finding works best for them, it's certainly an understood and accepted way of going about things, except for perhaps among the few closed-minded folks who think their way (of more openness) is the only real/right way.
I see poly-fi as definitely being different from mono. After all, you've discardeded the fundamental idea that only two people can love each other romantically at once. However, there is a similarity that doesn't exist in more open poly structures in that sexual and romantic exclusivity is equated with commitment. So, I see poly-fi as being poly, but a certain subtype of poly that does share at least one thing in coming with monogamy.
All that said, I really take umbrage at the suggestion that more open poly is equivalent to cheating. Maybe it would be in your relationship, but if others have set different rules, which they are following faithfully, then by definition they're not "cheating". It's dismissive and divisive to put it that way. It also just seems odd to imply that there's anything wrong with open poly when so many people find love, joy, and commitment within it.
Me, 30ish bi female, been doing solo poly for roughly 5 years. Gia, Clay, and Pike, my partners. Davis, ex/friend/"it's complicated." Eric, Gia's husband. Bee, Gia and Eric's toddler.