group A vs blood group

group A and blood group both are nouns.

Word	Noun	Adjective	Verb	Adverb
group A	Yes	No	No	No
blood group	Yes	No	No	No

As nouns, blood group is a hypernym of group A; that is, blood group is a word with a broader meaning than group A:

group A: the blood group whose red cells carry the A antigen
blood group: human blood cells (usually just the red blood cells) that have the same antigens

Other hypernyms of group A include blood type.

group A (noun)	blood group (noun)
the blood group whose red cells carry the A antigen	human blood cells (usually just the red blood cells) that have the same antigens