Of course your thoughts and question are necessary ones. When a distinction is made between Jew and Gentle/Greek we should keep this also in mind:
"Not as though the word of God hath taken none effect. For they are not all Israel, which are of Israel:" Rom 9:6
So is every physical descendant of Jacob a Jew... or even if he is, is he an Israelite?
The descendants of Jacob may still "supplanters" or "heel catchers".
ÅIsrahvl Israel (is-rah-ale');
Word Origin: Hebrew, Adjective, Strong #: 2474
Israel = "he shall be a prince of God"
- the name given to the patriarch Jacob (and borne by him in addition to his former name)
- the family or descendants of Israel, the nation of Israel
- Christians, the Israel of God (Gal 6:
KJV Word Usage and Count
Israel 70
ÅIakwvb Iakob (ee-ak-obe');
Word Origin: Hebrew, Noun Masculine, Strong #: 2384
Jacob = "heel-catcher or supplanter"
- was the second son of Isaac
- the father of Joseph, the husband of Mary
KJV Word Usage and Count
Jacob 27