I work as a Producer for an ad agency and recently had to to film an interactive quiz for a client. As producer, I had control over the project management, budget and resource management, and within this I had to source a film production company. They have their own producer whose job it was to source the actors, director, costumes, crew and studios.
This comprises of auditioning the actors for various roles, and choosing a Director - which was based on watching show reels from a selection of Directors to see who had the correct style to fit in with our brief.
Once the actors and directors were chosen, the TV production company producer books the studio, and ensures everyone is where they should be on the day, and that we have all the correct resources.
On the day of filming the TV producer is in control of the content, whereas the Director is in control of the actors, lighting, sound and cameramen, so the Producer and Director work fairly closely to ensure that they have every sequence required for the client.
As Producer for the ad-agency I was only required to be on set to make any executive decisions on behalf of the client, but apart from that it was my role to sit around and marvel at how long everything takes, how complex the lighting looks, and to eat all the complimentary food!