American flag vs Old Glory

American flag and Old Glory both are nouns.

Word	Noun	Adjective	Verb	Adverb
American flag	Yes	No	No	No
Old Glory	Yes	No	No	No

As nouns, American flag and Old Glory are synonyms defined as:

American flag and Old Glory: the national flag of the United States of America

Other synonyms of American flag include Star-Spangled Banner, Stars and Stripes.

American flag (noun)	Old Glory (noun)
the national flag of the United States of America	the national flag of the United States of America