Orthodox Judaism vs Jewish Orthodoxy

Orthodox Judaism and Jewish Orthodoxy both are nouns.

Word	Noun	Adjective	Verb	Adverb
Orthodox Judaism	Yes	No	No	No
Jewish Orthodoxy	Yes	No	No	No

As nouns, Orthodox Judaism and Jewish Orthodoxy are synonyms defined as:

Orthodox Judaism and Jewish Orthodoxy: Jews who strictly observe the Mosaic law as interpreted in the Talmud

Orthodox Judaism (noun)	Jewish Orthodoxy (noun)
beliefs and practices of a Judaic sect that strictly observes Mosaic law	Jews who strictly observe the Mosaic law as interpreted in the Talmud
Jews who strictly observe the Mosaic law as interpreted in the Talmud