Arabian Desert vs Eastern Desert

Arabian Desert and Eastern Desert both are nouns.

Word	Noun	Adjective	Verb	Adverb
Arabian Desert	Yes	No	No	No
Eastern Desert	Yes	No	No	No

As nouns, Arabian Desert and Eastern Desert are synonyms defined as:

Arabian Desert and Eastern Desert: a desert in Egypt between the Nile River and the Red Sea

Arabian Desert (noun)	Eastern Desert (noun)
a desert on the Arabian Peninsula in southwestern Asia	a desert in Egypt between the Nile River and the Red Sea
a desert in Egypt between the Nile River and the Red Sea