High Church vs religious order

High Church and religious order both are nouns.

Word	Noun	Adjective	Verb	Adverb
High Church	Yes	No	No	No
religious order	Yes	No	No	No

As nouns, religious order is a hypernym of High Church; that is, religious order is a word with a broader meaning than High Church:

High Church: a group in the Anglican Church that emphasizes the Catholic tradition (especially in sacraments and rituals and obedience to church authority)
religious order: a subdivision of a larger religious group

Other hypernyms of High Church include religious sect, sect.

High Church (noun)	religious order (noun)
a group in the Anglican Church that emphasizes the Catholic tradition (especially in sacraments and rituals and obedience to church authority)	a subdivision of a larger religious group