These terms overlap but are often distinguished in usage. In the older portions of the Bible the descendants of Abraham and Sarah are referred to as “Hebrews.” Since the 6th century BCE Babylonian captivity and the return from exile, they have been known as “Jews,” a name derived from the dominant remaining tribe of Judah. Modern Jews are seldom referred to as “Hebrews” but the language spoken in the state of Israel today, based on ancient Hebrew, is “Modern Hebrew.” Although “Hebrew” has sometimes been used in a condescending or insulting manner to refer to modern Jews, it is not in itself an insulting term. However, it is normal when you have a choice to use “Jew” to refer both to people of the Jewish faith and to ethnic Jews, religious or not.
“Hewbrew” is a common misspelling of “Hebrew.” If you’re in the habit of ignoring names when they are flagged by your spelling checker, don’t ignore this one.