Old Glory vs American flag

Old Glory and American flag both are nouns.

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

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

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

Other synonyms of Old Glory include Star-Spangled Banner, Stars and Stripes.

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