American flag vs Stars and Stripes

American flag and Stars and Stripes both are nouns.

Word	Noun	Adjective	Verb	Adverb
American flag	Yes	No	No	No
Stars and Stripes	Yes	No	No	No

As nouns, American flag and Stars and Stripes are synonyms defined as:

American flag and Stars and Stripes: the national flag of the United States of America

Other synonyms of American flag include Old Glory, Star-Spangled Banner.

American flag (noun)	Stars and Stripes (noun)
the national flag of the United States of America	the national flag of the United States of America