You know, this is interesting because it really brings out the problem you have with our language. We'd regard those two things as equivalent. "For, what I have pardoned, if I have pardoned any thing, for your sakes have I done it in the person of Christ" (2 Cor. 2:10). Similarly we speak of the priest as "alter Christus" (another Christ) because he acts in the person of Christ. I think you are simply overreading our words. We certainly do not mean this: that the Pope and Christ are one and the same! Then the Roman Catholics should have no problems worshiping the Pope, who is then considered "God" on earth. In fact, we say that the Pope "hold[s] upon this earth the place of God Almighty" (Leo XIII, Praeclara Gratulationis), not that he is God Almighty!
Really, no one over here has ever suggested worshiping the Pope as "Christ on earth", so that should give you a real understanding of how we are using these terms...
Or could it be the problems the West has with the Greek language? Greek translations say "in the presence of Christ." The word used in Greek original is "prosopon" which is to say face, the front of the human head, countenance, look, the appearance one presents, the outward appearance...and so on.
Judging what St. Ignatius wrote in his notes on-the-fly he, at one point, he gives that "appearance," that authority to all bishops, presbyters and even deacons, not just the successor of Peter, and even that might be a stretched translation.
But it's a great stretch to go from appearance to a person. When an actor plays a historical figure we do not say that the actors is the person he portrays. The actor is the icon of the person portrayed -- he merely makes us think of the person portrayed.
And, judging how some Popes behaved and acted, that's a stretch too.