The difference is that in polygamy it's focused on one person in the center with multiple spouses (polygyny if it is one male with many wives or polyandry if it is one female with many husbands); it's a harem. While in polycules, there is a mix and match of relationships, maybe a guy with multiple wives, but one of his wives is also in a relationship that the husband is not a part of. Even more confusing is that all the terms I've talked about in this paragraph are different forms of polyamory.
For example, in
Intimancer, the "straight" male MC dates a bisexual human woman who is also in a lesbian relationship with a dwarf; the MC had a harem of his human wife, elf wife, and succubus wife, while the human wife had the MC, the elf, the succubus, and the dwarf. Since MC didn't touch the dwarf and the dwarf didn't touch the succubus. The term "polygamy" doesn't fit, while "polycule" does.
Other series like
Monster Breeder and
A New Kind of Grind also portray relationships that don't fit polygamy.
Tags are supposed to be niche; maybe some readers love "polyandry" (woman with many lovers) but hate "polygyny" (man with many lovers) or vice versa, which makes the terms "polygamy" (person with undefined gender marrying many lovers) and "polyamory" (person of undefined gender in relationship with many lovers, may or may not involve marriage) too much of a blanket term. The tags are meant to make it easier to find stories you like and avoid stories you'd dislike.
I don't mind more tags as long as it's clearly defined when to use them.