The scorer gets the credit, but the player giving him the decisive pass is just as important. Both forwards and midfielders profit from being good at this.
Inner midfielders, and forwards contribute to the central attack rating by their passing ability. Wingers played offensively, normal or defensively use their passing to contribute to side attacks. There is some debate about the contribution of passing on a winger towards middle, with most people believing it aids central attack.
Passing is also very important for use with tactics. It helps to compute ratings for Counter Attack, Attack on Wings and Attack in the Middle.
In terms of the difference passing makes to your ratings, it is estimated that about 3 levels of passing will equal one level of scoring on a forward, or one level of wing on a winger.