Church as a building used for public Christian worship. According to Oxford’s Essential Dictionary, it comes from the old English word ‘cir(i)ce’ or ‘cyr(i)ce’ related to the Dutch word kirk or German word kirsche and was based on the medieval Greek word kurikon derived both from the Greek word kuriakon doma (Lord’s house) and kurios (master or lord).
Cathedral is defined as a church which contains the official seat of a bishop in the principal church of a diocese (the district in which the a bishop has ecclesiastical authority). Only the Anglican, some Lutheran, Eastern Orthodox, and Roman Catholic denominations have cathedrals. A cathedral is shaped like a cross, and its entrance faces west
Basilica as an ancient Roman hall used as a church and was the chief type of church built during the early Middle Ages and is usually shaped/designed like a cross.
Temple is a more general term describing any building used for the worship of a god or gods and now principally accepted to describe many ancient and prehistoric sites preceding Christ.