The Torah, aka the 1st 5 books of "Old Testament" does not use the term "Jew" or in Hebrew, "Yehudi" anywhere. I think this term first appears in the book of Esther. Otherwise, the most common term in the Torah is "B'nei Yisra'el", meaning "Sons (or children) of Israel", with Israel being the name given to Jacob. At any rate, in the Torah, the term "Israel" almost always refers to the nation, or what we now call "Jews". (FYI, in the Torah, the word "Israel" is never used to refer to the country itself. That name, is used after the land of Cana'an was settled.)
The term "Gentile" might be equivalent to the term "Goy" which is a generic term used to mean "nation" or "people" and that term is sometimes used for the nation of Israel, itself. It depends on its context. Usually, the Torah would refer to a nation of non-Jews by their specific national name such as Cananites, Hittites, Anakim, etc.
regardless, when the Torah refers to "Gentiles" or those that are non-Jews, it is closer to the 2nd idea - they were not born Jewish, as describe in my point, above. A Jew who does not practice his religion, and sadly, AFAIK, that's the majority in the world, currently, is still considered Jewish. Once you are Jewish you cannot "convert" out of it. Even a non-Jew that converted properly (there are "improper" conversions. Delve through this site for details on this notion) and became Jewish, remains Jewish for life.