In music the producer traditionally supervises the engineers and to some extent the artist. The producer explains what he/she wants, the engineers just implement it.

For example, artist comes in with guitar, a chord progression, and a song. Producers says 'let's plug your guitar in a Marshall Amp and mike the cab, then we'll double-track that with the direct signal.' Engineers goes and sets everything up, and at most makes suggestions on what sort of microphone to use or that this configuration sounds especially good with a bit of room sound, and takes care of setting up the mixing desk to avoid distortion on the recording and phasing between the direct and amplified signals.

Most producers start out as engineers rather than musicians. Their specialty is tone and mixing, which also feeds into song structure and arrangement.