Generally speaking “Israelites” refer to the ancestors of the Jews whose story is told in the Old Testament. In the book of Genesis, Abraham’s grandson Jacob was renamed “Israel”(Genesis 32:28) and following that renaming, Jacob’s descendants were commonly referred to as Israelites. It was centuries before the religion of the Israelites coalesced into the more unified practices we sometimes associate with Judaism in Jesus’ time. Even then there were many ways to practice “Judaism,” just as today there are a myriad ways that Christians practice Christianity. Consequently, it is more accurate to refer to Jesus’ (and our) distant ancestors in religion as Israelites, rather than Jews.