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.
A forward with defensive orders will contribute more of his passing skill to attack ratings than a forward with normal orders. This is further enhanced for a defensive forward with the technical specialty, to the point that it becomes that player's "primary skill", contributing more than any other skill to the team's ratings.
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.
What you should keep in mind with this exchange ratio is, if we look at the rules, that passing on a forward doesn't contribute to the wing ratings. Furthermore it's not clear whether passing on a forward toward wing is shifted to the wing attack.
Passing does, on the other hand, assist in salary management. The difference in salary between two similarly-rated forwards, one with excellent scoring and disastrous passing, the other with solid scoring and weak passing, is negligible. However, the salary difference between an extra-terrestrial scorer with disastrous passing and a supernatural forward with solid passing is very significant.