MaxG is right, that a producer is like a coach, but like a coach they bring along their own style.

Listen to Cream's 'Fresh Cream' produced by Robert Stigwood and then listen to all the later albums produced by Felix Pappilardi. There is a definite change in the sound. Then listen to a group called Mountain. Felix Pappilari produced their albums as well as played bass.

There are more modern examples of producer 'sound' but I used that example because both groups had hits and were successful.