Israel vs State of Israel

Israel and State of Israel both are nouns.

Word	Noun	Adjective	Verb	Adverb
Israel	Yes	No	No	No
State of Israel	Yes	No	No	No

As nouns, Israel and State of Israel are synonyms defined as:

Israel and State of Israel: Jewish republic in southwestern Asia at eastern end of Mediterranean; formerly part of Palestine

Other synonyms of Israel include Sion, Yisrael, Zion.

Israel (noun)	State of Israel (noun)
Jewish republic in southwestern Asia at eastern end of Mediterranean; formerly part of Palestine	Jewish republic in southwestern Asia at eastern end of Mediterranean; formerly part of Palestine
an ancient kingdom of the Hebrew tribes at the southeastern end of the Mediterranean Sea; founded by Saul around 1025 BC and destroyed by the Assyrians in 721 BC