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)
The caption to the photo identified the firefighters as "firemen".
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")
In 2384, aboard the USS Dauntless, firefighting was a section in Security, and the firefighters were assigned to squadrons. That year, four firefighters from Squadron 5 were working in concert with the fire fighting system to extinguish a fire in the shuttlebay. The fire had started in the starboard warp nacelle of a Type 9 shuttlecraft. This situation was being monitored from an operations console on the bridge. (PRO: "Mindwalk")
A clear view of this operations console from the bridge was provided by Dominique Rossier of Wardenlight Studio. [1]