Judaism vs Jewish religion

Judaism and Jewish religion both are nouns.

Word	Noun	Adjective	Verb	Adverb
Judaism	Yes	No	No	No
Jewish religion	Yes	No	No	No

As nouns, Judaism and Jewish religion are synonyms defined as:

Judaism and Jewish religion: Jews collectively who practice a religion based on the Torah and the Talmud

Other synonyms of Judaism include Hebraism.

Judaism (noun)	Jewish religion (noun)
the monotheistic religion of the Jews having its spiritual and ethical principles embodied chiefly in the Torah and in the Talmud	Jews collectively who practice a religion based on the Torah and the Talmud
Jews collectively who practice a religion based on the Torah and the Talmud