The most explained moment in the choreography is the removal of the omophorion before the reading of the Gospel. The reason given is that Christ is then present and speaking directly, so the bishop lays aside the sign of his own representative office for the duration of the reading, and stands as one of the listeners. It is put back on afterwards. The same logic governs other removals and resumptions at points in the liturgy, and a server whose whole task during a hierarchical service is to hold, fold and present the omophorion at the right moments is a normal feature of a cathedral sanctuary.
Set beside the Latin pallium, the omophorion shows what a shared origin can come to mean in two places. Both are shoulder bands, both are wool, both are read through the shepherd carrying the sheep, and they are historically related. The western band narrowed steadily over the centuries into a thin circlet with pendants and became a privilege granted from Rome to metropolitans, expressing a relationship of jurisdiction. The eastern band stayed broad, stayed with every bishop, and expresses the episcopal order itself.
Two churches took the same piece of cloth and made it carry two different ecclesiologies, and both can point to the same parable while doing it.