Judaism and Christianity are two very different religions, having two very different Gods. In fact, Judaism has more in common with Islam than Christianity.
The monotheism of Judaism and Islam is very similar, the montheism of Christianity is very different. Yahweh and Allah were remote, distant, impassable, deities, in Christianity, God became out savior - which is what the name Jesus means. Yah-shua, God (is become our) savior.
The type of monotheism of the Puritans was Christian, not Jewish or Islamic.
Maybe this will help. There are three names used in the New Testament to designate this people, (1.) Jews, as regards their nationality, to distinguish them from Gentiles. (2.) Hebrews, with regard to their language and education, to distinguish them from Hellenists, i.e., Jews who spoke the Greek language. (3.) Israelites, as respects their sacred privileges as the chosen people of God. “To other races we owe the splendid inheritance of modern civilization and secular culture; but the religious education of mankind has been the gift of the Jew alone.” Amen.