There are many people that quickly become confused about the different names of Roman Catholic Church buildings. This is even true for practicing Catholics. Many of the designations were handed down through the centuries, and many of them originally came from Rome. The Romans had many descriptions for buildings, whether or not they housed churches. Because Rome dominated the church for centuries, what the Romans called a building became common usage.
Basilicas were originally Roman meeting halls and not churches at all. They were large public buildings that had three main areas. Their original purpose was for large gatherings of people indoors. Some were used for indoor markets. Others were used as the local courthouse. No matter their use, they were not sacred buildings used for worship services. Once Christianity became legal, many churches were built in the same form because it was a convenient way to gather a large congregation for services. An altar was placed at the junction of the three areas and the building was consecrated as a church.
Churches and cathedrals are both churches. The only difference between them is that the church used by the local bishop is called a cathedral. This is the administrative church within the diocese and the bishop sits in the sanctuary on a throne. The cathedral has no other important religious designation and services are held in the same manner as any other church in the diocese.
Today there are many different Christian sects that have broken away from the Roman Catholic Church. Many parishes and churches are small enough that only a church building is needed. Some sects have only one church and are loosely aligned with a group of churches that practice more or less in the same manner. They have no use for cathedrals and have never called their church buildings basilicas. Even larger aligned Christian groups tend to avoid the building designations used by the Roman Catholic Church.