There are churches, and there are cathedrals. In fact, a “cathedral” is just a specific type of church, and was originally called a “cathedral church”.
The distinction — and in fact the word — only exists in particular Christian sects. Those sects would be the ones with an elaborate organizational hierarchy. And although the typical notion of a “cathedral” is that it’s a bigger, fancier church, the building doesn’t really have anything to do with it. Any church can be a cathedral. In fact, sometimes a regular church becomes a cathedral while looking exactly the same. And it works the other way around too; sometimes a cathedral becomes just a regular church — again, without lowering any spires or changing the number of stained-glass windows.
The key to whether a church is a cathedral has to do with a particular piece of interior furniture. A chair. The word “cathedral” comes from “cathedra,” which is the Latin word for “chair.” It’s not just any chair, though; it’s the chair (or throne) designated for the regional manager of the religious organization. In most Christian sects with that kind of hierarchical organization, the regional manager is called the “bishop.” The bishop is in charge of all the churches in a given area, and one of them is his regional headquarters. That’s where his “throne” is located, and that church, regardless of what it looks like, is the cathedral for that region. In Catholicism, the region is called a “diocese,” from the Latin “diocēsis,” which means a governor’s jurisdiction.
The bishop could (theoretically; there are probably a lot of rules about this) decide to move his regional headquarters to any other church in his diocese. That would automatically make the new location the cathedral, and the old one would revert to being jus a church.
Given the way human hierarchical organizations typically work (or fail to), influence and material wealth accumulate wherever the power is located. It’s the same with cathedrals; they’re bigger and fancier than the other churches because they’re the “seat” (get it?) of power. Parishioners (a “parish” is the province where a church is located; it’s another Latin-derived term) donate money to their local church, and each local church channels some of that money to the cathedral, where it’s up to the bishop to decide what to do with it. At least in ages past, one of the job qualifications for being a bishop seems to have been having a keen appreciation for fine, expensive craftsmanship in stone, wood, marble, gold, and stained glass. Thus cathedrals kept getting upgraded. And, of course, each upgrade would come with a fancier chair.
