The only head of the Church is our Lord Jesus Christ. On earth, the Church is where the bishop is, the clergy and laity. Each individual church is a full Body of Christ (i.e. represents fullness of faith and sacraments). This is the original Church organization.
A bishop is an Apostolic minister, whose spiritual authority can be traced by direct lineage to one of the twelve Apostles. Bishops who share the same faith (theology) are in communion with each other.
One of them is given the honor of being their spokesman and a chosen spokesman and representative of their communion, who is considered "first among equals," or "first in love" but not in authority; he has no legal authority over other bishops.
Ecclesisastical, theological and other church matters are decided by a synod or council of bishops, with the "first among equals" having the same vote as others. He has some privileges such as to convene a Synod, and he presides over a Synod, and his words are taken with reverence because of his role, and so on.
Orthodox Church is a group of "self-headed" (autocephalous) Orthodox Churches, each headed by a Patriarch or an archbishop. A patriarch is first among equals in a local (usually national) Church. Some national churches have what is known as Metropolitan in Slavic and Archimandrite in Greek churches -- basically an archbishop. The fourteen patriarchs are in communion with the Bishop of Constantinople, and together with him form a Synod of the Orthodox Church. He represents the Orthodox world, but is not the "leader" of the Orthodox Christians as he is often portrayed in the western media.
Hope this helps.
Yes, that is very helpful. Thank you very much for your answer. The way you described the "first among equals" idea reminded me of the Chief Justice of the SCOTUS. He has some additional administrative functions and has some extra influence over some things, but he still has only one vote. Is that a fair or accurate comparison? So if the Bishop of Constantinople is like this, then the Bishop of Rome is really more like a king?