The likely word sought is "chapel" which is also used for a religious area within other types of buildings (e.g. hospitals, prisons).
1-300 members?
A cathedral is the name of the principle church of the diocese. This is a very large church that is of great importance.
A diocese means a collection of churches that exist in the same geographical region. It is headed by a bishop. The main church is called the Cathedral because it has the bishop's chair in it (called the Catherda) \
An area of land (usually county-sized) that is supervised by a bishop is called a diocese. The most important church within a diocese where the Bishop's throne is situated (the 'cathedra') is called a cathedral. Any church within the same denomination and diocese is a 'diocesan church' in the sense that it belongs to that diocese. As an example, in an Anglican diocese, all Anglican churches are diocesan churches, but Methodist, Baptist, URC etc churches, even if they are within that diocese, are not.
The Pope is the temporal leader of the Catholic Church, and a Bishop has power over a small portion of the world [called a Diocese], but he must ultimately answer to the Pope.
A diocese is the local area of the Church led by a bishop.
I believe you are describing a "Mission".
He rules an area with several churches called a diocese
The head of a diocese is called a Bishop, or if it is an important diocese, an Archbishop. Some diocese are headed by a Cardinal, but that is just the designation of a Bishop or Archbishop who also serves an elector of the new pope.
Diocese of Connor - Church of Ireland - was created in 1944.
Your question reveals an ignorance of what "the Catholic Church" is. Each individual bishop rules a diocese, and each diocese is an autonomous Catholic Church. Even the Pope is just the Bishop of Rome. Thus each individual diocese contributes whatever its Bishop decides to use to support the individual Caritas in his diocese or his country, you would have to check with each individual diocese or archdiocese, of which there are 2,845 "particular" Churches, which, together, are collectively called "The Catholic Church".
Actually, no. St. Paul's is theCathedral of the Church of England in the Anglican Diocese of London..The Roman Catholic Cathedral located in London is called Westminster Cathedral, seat of the Archbishop of the Westminster Diocese.Both the Anglican and The Roman Catholic Church are divided geographically into areas called "dioceses". Each of the dioceses is overseen by a bishop, who in the case of the Catholic church, is appointed by the Pope. Whichever church in the diocese the bishop lives at and regularly says Mass at is called the cathedral for that diocese.
Church