Depends on the department. If the department runs fire and ems together or separate, or if all their ambulances are BLS or ALS or a mix of the two. Some departments have their medics who are also firefighters on engines or rescue companies and are only really pulled off the rig if another medic is not available. other than that you'll have to investigate the dept's your interested in and their SOP's.

Statistically, firefighters are dispatched for medical response about 80% of their calls. They are typically located closer, and are the first responders to 911 medical calls, usually turn the event over to an ambulance service and don't provide transport.

Where I live (Ventura County, which is unusual is this respect), all the firefighters must have paramedic certification, and the same firefighters respond to fires and medical calls. (This reduces the total number of personnel who must respond when there is a car accident, and they do not know if it is going to cause a fire or a medical problem.) As a result, no one without paramedic certification fights any fires in places where only the county fire department fights fires. (However, some cities, a military base, and a national forest may have their own fire departments.)

I am not aware of any other county with that policy.

When someone it trapped in a fire in any county, it is likely enough that they will be injured by the time that they are rescued that the ambulance and paramedic fighters are likely to be sent (even though the person trapped in the fire might actually be uninjured or dead). If the person is still in the fire when they arrive, or the person is dead or uninjured, they probably help fight the fire until there is something else for them to do. I doubt that they just sit around. (However, they would probably fight the fire from the outside, by spraying water on the building, not go inside, because they could be needed if someone comes out of the building injured.)

In very small towns, or very rural areas, where there are only 2-4 total firefighters (paramedic and otherwise) on duty at a time, they may all go to all the calls (medical and fire), so that they are together in case there is another call that requires a large response.