The game mode where teams fight to deliver a Rainmaker is called Rainmaker.
Rainmaker is an objective-based Ranked Battle mode in which both teams compete for a powerful weapon placed near the center of the stage. A team must break the Rainmaker’s protective barrier, then have one player pick it up and carry it toward the opponent’s goal.
The carrier can fire the Rainmaker as a weapon, but cannot simply hold it indefinitely. If the carrier is splatted or leaves the playable area, the weapon drops; after it is not claimed, it eventually resets. In Splatoon 3, the route also includes checkpoints, adding extra defensive positions to the push.
A common mix-up is confusing the weapon with the mode. “Rainmaker” is both the name of the large weapon and the official name of the game mode. Clam Blitz uses Power Clams, Splat Zones focuses on controlling marked areas, and Tower Control requires escorting a moving tower.