A church is basically, no matter the religion, is a general place of worship where sacrements can be proformed and where (atleast in Roman Catholicism) the bread and wine become flesh and blood.
A cathedral, on the other hand is the (usually) the biggest church in the diocese. It is the seat of the bishop of that diocese, and usually in the biggest city or part of that diocese. Take for instance Saint Patrick's Cathedral in NYC. This is quite large, and though it is a parish, it is also where the bishop resides.
