The term 'producer' is one of the most elastic adjectives in the music industry.
A lot of producers are expert engineers and they will shape the whole aural spectrum of a record.Others are 'organisers' and arrange studio time, musicians, instruments, orchestra sessions and so on. Some are 'inspirational' - including Quincy who told MJ that three of the songs for Thriller were not good enough and he should write three more - one of the replacements wa 'Billie Jean'!
Jagger and Richard produce The Stones' albums, and the way they work is to noodle about in the studio until they get an idea, and work it into a song. J & R decide if the end result is good enough for the album.
t does vary a lot - there are no real hard and fast rules.