What is the difference between a cathedral and a basilica?
Then, what makes a church a basilica?
A basilica is a church with certain privileges conferred on it by the Pope. Not all churches with "basilica" in their title actually have the ecclesiastical status, which can lead to confusion, since it is also an architectural term for a church-building style. Such churches are referred to as immemorial basilicas.
Simply so, what is the difference between a cathedral and a church?
The cathedral is a much larger place of worship than a church and is run by a bishop. A church is run by a group of clergymen or priests. The bishop usually resides on the cathedral premises.
A church becomes a cathedral when a cathedra is placed within it. A cathedral holds a cathedra. A cathedra is a permanent seat/chair/throne/bench upon which a bishop sits during services. A cathedral holds a cathedra, and a cathedra is only put into churches which serve as a bishop's church.