Answer:
The simplest answer is it's the difference in legality. I live in a polyamorous relationship termed poly-fidelity. I have my wife and our live in 3rd who has been with us exclusively for several years. But because she cannot legally marry me/us, she is not recognized under the laws of the US as entitled to anything, benefits or rights, that a married woman would normally have.
In Africa where it is legal to have more than one wife, they practice Polygyny when a man legally marries more than one woman.