"Noun. side chick (plural side chicks) (African American Vernacular, slang) A mistress; a woman one dates in addition to one's girlfriend or wife, usually (but not always) in secret."
That is the common understanding of the term.
It's different from seeing other parties while in an open relationship because that's just... exercising an open relationship. There are open relationships that are effectively monogamous because the couple isn't seeing or sleeping with other people at the time, even though they're down for it. Sleeping with someone else while in a relationship where it's allowed is just considered "poly", not having a side piece.
Side piece is damn near always used in reference to adultery.