A firefighter or fireman was an individual trained in fighting fires (firefighting). Individuals aboard starships responsible for said duties was identified as a fire control party or fire control personnel.
In 1893, as Data walked down Putney, a firefighter attached to No. 5 Fire House was doing maintenance on a fire engine. (TNG: "Time's Arrow")
In 1986, a photo of firefighters fighting a fire at the Fairmont Hotel was on the front page of the San Francisco Register. (Star Trek IV: The Voyage Home)
Emergency procedures placed on the doors aboard the freighter ECS Fortunate gave instructions when the fire control personnel should be alarmed. (ENT: "Fortunate Son")
In 2364, while re-living the 2355 Battle of Maxia, Jean-Luc Picard recalled ordering Vigo to have a fire control party dispatched to the bridge of the USS Stargazer. (TNG: "The Battle")