I've noticed that people in the orthodox community tend to call themselves "religious Jews." I really don't like this phrase. I'm not happy with the phrase "observant Jews" either, but I haven't found a better replacement. (I'm open to suggestions if you have any!) And if you're thinking of using the term "orthodox Jews" instead, that's not quite the same meaning either.
Why do I dislike the phrase "religious Jews" so much? While Judaism has a very specific meaning about what determines one's "religiosity" (one's actions), modern American society, thanks to Christian influence, thinks of "religious" as being a measurement of one's beliefs. For secular or liberal Jews who were not raised in "religious" homes, they probably (at least subconsciously) think of the modern secular definition of "religious." I can't stand the idea of accidentally implying that another Jew doesn't believe in G-d or have other Jewish religious beliefs. This is why I avoid the phrase and why I dislike its use in conversation. It's so easy to misinterpret, both by the "non-religious" Jews and non-Jews.
Why is "observant Jew" not much better? It still implies that other Jews aren't observant to our standards. Worse, it denies the observances/mitzvahs that other Jews do, even if they aren't doing all of them. There are reform and conservative Jews who are "observant" of some of all of the mitzvot (measured by Orthodox standards), even though they may or may not observe them exactly like the orthodox do (and there are probably serious discrepancies between orthodox groups' observances as well - see Rule #42 of Orthodox Conversion: There ARE Double Standards. Get Used to It.). Along the same lines, I dislike the phrase "Torah-true Judaism." Neither of these terms will foster communication or happy feelings from the person implied to be "not observant" and "Torah-untrue."
Jews are Jews are Jews, and I wish we could stop the semantics that divide us. The Jewish People could benefit from more conversations that avoided labels.