Jewish religion vs Judaism

Jewish religion and Judaism both are nouns.

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

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

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

Other synonyms of Jewish religion include Hebraism.

Jewish religion (noun)	Judaism (noun)
Jews collectively who practice a religion based on the Torah and the Talmud	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