[quote="commenter, post:11, topic:355666"]
I would also add that some archbishops have no see of their own, other than a titular see. They serve in administrative functions of the Holy See, or are papal nuncios to some countries. I think all archbishops receive the pallium, which I believe is a symbol of their special teaching responsibility, even if they never are ordinary of a diocese. They continue to be archbishops even if they retire or their archdiocese no longer exists. It is a lifetime designation. It is not specific to a specific job assignment or local church. That is a significant difference between Catholic and most Protestant leadership.
The Pallium is the sign of Metropolitan Authority within the Roman Church. It is historically occasionally given to non-metropolitan bishops, but that's not current practice. Further, except at the mass it is given at, it may only be worn in one's own province (if a metropolitan archbishop) or see (if a bishop). Or so note both the old Catholic Encyclopedia and also Inside the Vatican.
There is no direct equivalent in the eastern churches, but it's worth noting that the Omophorion of the Byzantines and the Syrian Batrashil are both related to the same prototypical garment, and similar in meaning. In fact, if one looks at the Pallium of HH Benedict, it was nearly identical in form to a Classic Byzantine Great Omophorion. But all byzantine bishops wear the Omophorion, and IIUC, all syrian bishops the Batrashil.
Note that there are 3 forms for the omophorion - The classical one - called the "Great Omophorion" - very much like a long stole, worn like HH Benedict wore the Pallium, but usually a bit wider; The Short Omophorion, worn around the neck, much like a roman priest's stole, but over the vestments; and the "Y-shaped" ones, which are a stylized variation upon the Great Omophorion, and worn in the same circumstances.