It’s my understanding that it becomes an issue for the Orthodox Church if an individual seeks to be married again after a previous marriage ends (otherwise, there isn’t a sacramental question). The bishop of that Diocese will receive a letter from the priest who is to conduct the wedding of that individual and will then either grant or deny the request for a second marriage to be performed.
I understand that the second marriage ceremony is actually different from the standard and includes prayers of repentance for the first marriage.
I believe you’re correct.
It’s important to understand, though, that the Orthodox Churches do NOT require a declaration that the first marriage never really existed before approving a second marriage. Thus, they hold that either a) the first marriage somehow ended before one of the spouses died, or b) that it is OK to be in more than one marriage at a time.
Neither of those two possibilities conforms to Catholic doctrine and therefore, neither of them is a suitable model for the Catholic Church to follow.
I think it is unfortunate that the Orthodox churches are known by that name. The word Orthodox means “right believing”, and they are not “right believing” in this matter or in some others. They are closer than most Protestants, but don’t forget that they are schismatic and therefore, no longer forming part of the Catholic Church, have lost the charism of infallibility.