Actually, not all metropolitans are heads of Sui Iuris churches. Metropolitan is the eastern norm for contracting “Metropolitan Archbishop”; the western norm is to contract it to Archbishop. The dozens of Ukrainian metropolitans, for example, do not head churches sui iuris.
Funtionally, the grades of bishop:
Pope
Eastern Patriarchs of Sui Iuris Churches
Western Patriarchs
Primatial Metropolitans of Sui Iuris Churches
Archbishop, Metropolitan
Bishop Eparch
Auxiliary Bishop, Auxiliary Archbishop
Of these, only auxiliary bishops and Auxiliary Archbishops lack vote in council/synod
With a handful of latin-rite exceptions, almost all archbishops & metropolitans head an ecclesiastical province consisting of their archdiocese and its suffragan dioceses.
Western patriarchs are archbishops with very important povinces.
Eastern Patriarchs have metropolitans and bishops both as suffragans
Major Archibishops are functionally patriarchs, but do not have the honorifics. (Well, HB Lubomyr has been accorded them by his own synod, and most of the church calls him Patriarch, even tho technically he’s “just” a major archbishop.)