Having no experience in either industry, this part
left me wondering. What's the difference between a
film producer and a music producer?

Offhand, a film producer is kind of the "owner" / executor / whipcracker of the film, who brings together the money, personel, necessary to make the film happen, and generally has ultimate creative say (also gets ultimate blame for bombing).

"Music producer" has a bit wider range of meaning I think. More classically, it refers to a role similar to the aforementioned but for records instead of film; the supervisor and organizer of the recording, mixing, mastering, budgeting etc.. But since the advent of digital music, PCs capable of (theoretically) nearly anything of a million-dollar studio, and softs like Pro Tools, Cakewalk, Ableton Live, and Reason, "producer" has evolved divergent to mean, especially in the realm of "techno" / "dance" / "electronic", (talk about persistent inaccurate lexicon) "The sole individual in charge of writing, performing, recording, arranging, mixing, and often mastering of the music." Some early famous instances might include Paul Oakenfield, DJ Shadow, and Aphex Twin. Producer aliases sometimes have the "DJ" tag in them, which can be a little misleading sometimes, as a DJ primarily just refers to the person in charge of selecting tracks and running turntables or whatever technology is playing the tracks, and a DJ may not "produce" any original material. Many producers, however, tend to DJ their own material (Aphex Twin has said that when he "DJs" live shows, he likes to challenge himself by attempting to duplicate, in realtime, the knob-twiddling / hacking the sound of his recordings).

i'm probably more of less going to repeat what TM said in a different way. but for me, you can be much more conscious of a record producer's influence. they can be the person that sits behind the mixing desk, hits record, affects levels, stuff like that. like TM says, its changed times, but in the past you could decide not to buy an album entirely on the producer, because you knew they would make a mess of it, that every album they did would sound like mud.

not sure that a film producer can have the same impact on a body of work, whether you can point a film and say "well that was obviously produced by X". though certainly, it seems, hollywood would have us believe that the producer really makes a difference to the end product - since they keep advertising films "from the producer of the matrix" or something.

so i guess the record producer is more like the film director. to a degree.

Yeah that's pretty accurate.

Though the "hats" people take on can mean a lot of different things even from project to project, and different individuals have different approaches. Some producers like to stay the hell out of the way of the artists / directors, give them maximal creative design space to work in; auterism. Others, especially major Hollywood producers, can be micromanaging controllers, shifting the job of the director to "make-my-shit-happen-guy" in which case the director has relatively little input. (Ala Kahn's rant)

I guess similar variance comes up between the record producer and artist. Some producers try to be instrument extensions of the artists, acting as facilitators/optimizers of the artist's vision and work. Others have more of a creative presence, and musicians may actively seek out a specific producer to give their album that unique sound (Brian Eno comes to mind).

The music producer may be closer in some senses to the cinematic equivalent of a post-production artist/technician team. Like the high-speed compositer who takes the rough footage of people jumping around on wires (samples) tweaks it, fashions out the spinner cam bullet-time, hands it off to the lighting/rendering guys and finally back to the head editor who takes the work to completion (mastering).

Film producers are business managers, music producers are creative partners.