Who is considered party to a case? Who can become party to a case?

Where I am, the state/DCF care provider is a party to the case, the GAL program is a party to the case, and each of the biological parents are a party to the case. Here, I believe anyone "with an interest" in the case can file a motion to intervene (ie, become a party to the case). The judge can either grant or deny the motion. I don't know how much this varies from state-to-state.