A church is a cathedral only if the "bishop ordinary" of that diocese (not a bishop without jurisdiction) has officially named it a cathedral. In the Roman Catholic Church, this is the usual practice. In other episcopally-governed church bodies or denominations, the bishop may make such a designation but, for various reasons, often does not.
In some instances, the the building/church is designated a "pro-cathedral" by the bishop ordinary rather than a cathedral. This is normally done as a prelude to raising it to the status of a cathedral. In Anglican jurisdictions, if there are assisting bishops, they are likely not to live in the same locality as the bishop ordinary, meaning that their own churches--despite being pastored by a bishop--are not cathedrals. And in Eastern Orthodox and Oriental Orthodox church bodies, the term is normally not used at all except in a casual way.
Many people refer to any very large church building as a "cathedral," whether or not a bishop is in residence and irrespective of the official practices of the denomination in question.--Wycliffe 11:20, 18 December 2010 (EST)