The appellant in the new case can be either the plaintiff (or claimant), defendant, third-party intervenor, or respondent (appellee) from the lower case, depending on who was the losing party.
The appellant has the opportunity to present arguments for the granting of the appeal and the appellee (or respondent) can present arguments against it.
It held appellants had ample legislative authority it could exercise to stop appellee's war making, and thus, appellants lacked the power to challenge such executive action in court.