In Little Rock, there was the main ambulance service (county funded, but privately managed) and two or three private ambulance services who mainly did point to point transport (like nursing home to hospital, hospital to hospital, etc). They were all run out of their own offices, and dispatched through 911 or had direct phone numbers. Fire rescue, a separate function related to ambulances (they only do truly dangerous stuff, I understand, and not much transportation of patients) was housed in and run by the city fire department. Also, they apparently do the 'medical, but won't need transport' stuff, like when DP fell coming home from the hospital and we couldn't get her in the house (too much anesthesia and too soon after surgery to release her). WONDERFUL. Took three of them to get her up (she was still re-learning how to walk and wasn't much help).
In Buford, GA, where we live now, the ambulances are owned by and run by the county, and are housed and dispatched from the fire station. They roll both an ambulance and a fire truck to all emergencies, where possible. They were SO nice when I had to call them during DP's 105 fever delirium - I was afraid they'd think we were nuts, but I was afraid to transport her, for fear she'd start seizing. The fever had gone up 1 degree in 30 minutes, and it was a 40 minute drive to the nearest ER.