As I understand it, we Orthodox see ourselves as an extension of the Lord's resurrected body in a very direct sense.
Yes, I think that is a real difference between us - though I hasten to add that it is not a concept which should be allowed to cause a rift or breach of fellowship between those who truly belong to Christ. I confess that the Orthodox concept to which you refer is one aspect of Orthodoxy which I have not yet been able to penetrate with my understanding.
If I may make a comment; This is a good spot to understand our differences on several levels.
So if I understand correctly, for you those in your Church are in agreement with Christ, believe in him and follow him as your example and Lord. It is a concept you follow, a Principle of faith. Christianity is agreement in Principle and if you follow a certain bundle of Principles, you are Saved.
For Orthodox, we are actually, in a real sense, both physically and spiritually joined to Jesus Christ. Just because we believe this is so does not make it just a "concept" or idea or a Principle. It bespeaks a totally different paradigm, Faith by Principle vs. Faith via Concrete Manifestation
( we are ACTUALLY joined to Christ). Manifestation by Principle vs Actual Manifestation.
We see this played out several places. You see the Eucharist as Symbolic, reaffirming your idea's ( The Principles you adhere to) and giving inspiration. We see the Eucharist as ACTUALLY Christ, Body Soul and Divinity which we consume taking him into our bodies via a physical act.
We practice two different types of Religion.
So to you, our concept of The Church is an idea we have and your concept is an idea you have that we can agree to disagree on. No big deal.
But I would like you to see that this goes far deeper and reflects two very different World Views that your approach can easily reconcile ( "Your Okay, I'm Okay", it's just a different concept) but we cannot.
Much of what we do does not compute with you because your basis of understanding uses a filter that does not account for a different Type