Protestant vs Christian church

Protestant and Christian church both are nouns.

Word	Noun	Adjective	Verb	Adverb
Protestant	Yes	Yes	No	No
Christian church	Yes	No	No	No

As nouns, Christian church is a hypernym of Protestant; that is, Christian church is a word with a broader meaning than Protestant:

Protestant: the Protestant churches and denominations collectively
Christian church: one of the groups of Christians who have their own beliefs and forms of worship

Other hypernyms of Protestant include church.

Protestant (noun)	Christian church (noun)
the Protestant churches and denominations collectively	one of the groups of Christians who have their own beliefs and forms of worship
an adherent of Protestantism

Protestant (adjective)	Christian church (adjective)
of or relating to Protestants or Protestantism