Jew vs Israelite

Jew and Israelite both are nouns.

Word	Noun	Adjective	Verb	Adverb
Jew	Yes	No	No	No
Israelite	Yes	No	No	No

As nouns, Jew and Israelite are synonyms defined as:

Jew and Israelite: a person belonging to the worldwide group claiming descent from Jacob (or converted to it) and connected by cultural or religious ties

Other synonyms of Jew include Hebrew.

Jew (noun)	Israelite (noun)
a person belonging to the worldwide group claiming descent from Jacob (or converted to it) and connected by cultural or religious ties	a native or inhabitant of the ancient kingdom of Israel
	a person belonging to the worldwide group claiming descent from Jacob (or converted to it) and connected by cultural or religious ties