Complete this analogy – Protestant : denomination :: Jew : ?

You might get that answer if you ask an Ashkenazic Jew. If you ask a Sephardic Jew, you may get an answer in Ladino instead.

Doc Cathode’s analysis is spot-on, if a bit America-centric (Israeli Jews tend to consider Haredim and “knitted-kippa” Orthodox to be seperate “streams”).

What you have to remember is that most Jews consider all Jews to be members of the same religion, regardless of how they choose to worship - or if they choose to worship at all. For instance, call myself a Conservative Jew, but what I mean is that I’m a Jew who generally agrees with the beliefs and customs of the Conservative movement, and who prefers to go to a Conservative synagogue. To use the OP’s rubric, Religion : Branch :: Citizenship : Political Affiliation.

I’ve heard “branch”, “denomination”, and “movement” all used, pretty much interchangeably.

I want to point out that that’s not necessarily true for a convert to Judaism, such as myself. I converted Conservative, so would not be considered Jewish by Orthodox Jews. If I wanted to join an Orthodox synagogue, I would have to undergo another conversion. Reform, Reconstructionist, and Jewish Renewal recognize Conservative conversions, so I wouldn’t have to convert again if I wanted to join one of their synagogues.

For Christianity, that would depend on, perhaps among other things, the communion rules for the denomination in question.

So do most denominations of Christianity- they recognize denominational differences, but they do think of people in those other denominations as Christian. The exceptions to that are mostly the lunatic fringe, like Jack Chick.

The important thing is whether your conversion included a promise to observe all the commandments. If it did, then the Orthodox will recognize it as valid.