coloured person vs blackamoor

coloured person and blackamoor both are nouns.

Word	Noun	Adjective	Verb	Adverb
coloured person	Yes	No	No	No
blackamoor	Yes	No	No	No

As nouns, blackamoor is a hypernym of coloured person; that is, blackamoor is a word with a broader meaning than coloured person:

coloured person: a United States term for Blacks that is now considered offensive
blackamoor: a person with dark skin who comes from Africa (or whose ancestors came from Africa)

Other hypernyms of coloured person include African-American, Black, Negro, Negroid, Black person.

coloured person (noun)	blackamoor (noun)
a United States term for Blacks that is now considered offensive	a person with dark skin who comes from Africa (or whose ancestors came from Africa)