Catholic church and Christian church

Catholic church noun - Any of several churches claiming to have maintained historical continuity with the original Christian Church.

Christian church and Catholic church are semantically related. In some cases you can use "Christian church" instead a noun phrase "Catholic church".

Christian church noun - One of the groups of Christians who have their own beliefs and forms of worship.

Catholic church and Christian church are semantically related. Sometimes you can replace phrase "Catholic church" with "Christian church", this phrases are similar.