Question: What I mean is that religious Jews often use words like shabbos, mitzvot, teshuvah, siddur. Why not use the English words, Sabbath, laws, repentance/penance, and liturgal order (for example)?

After all, no two languages converge and represent each other perfectly or exactly, yet we usually submit to the compromise of [/the compromise that is] translation.

I feel like I'm missing something?

Thanks in advance.

Answer: 
A few reasons come to mind why Hebrew/Aramaic/Yiddish (HAY) terms are often used:

1. Sometimes there are nuances to the terms that are more readily captured by the Hebrew/Aramaic/Yiddish term than the English translation. *Shabbat* denotes Saturday in a Jewish (or Israeli) context, as opposed to (*lehavdil*) Saturday, which is a secular day, or Sabbath, which may have a Christian flavour. A *siddur* is a Jewish prayer book used for daily prayer, and for some holidays. This is not quite the same as a *machzor*, a *bentcher*, a *haggadah* or a *tiklal*.

* In halakhic matters, it is common to use technical terminology from the Talmud or other rabbinic works where these matters are discussed. In modern Law, Latin terms are similarly often used in part because historically, Latin was the *lingua franca* of legal discourse. Just as a lawyer says *a fortiori*, a Yeshiva bochur may say *kal vakhomer*.

2. HAY terms can be prestige markers, since they are reflect education of the speaker. This is analogous to the situation in Yiddish, where Aramaic words and phrases are used far more frequently by (primarily men) educated in halakha.
3. HAY terms can be used to distinguish Jewish religious terms from secular terms or analogous terms in other religions. I already mentioned how *Shabbat* (or *Shabbes*) can be used in contradistinction to *Sabbath*. *Bible* is another example of a term often associated with Christianity, which is why some Jews prefer *TaNaKh* or *mikra*. Some terms can even be used by Jews to distinguish themselves from other Jews. For instance, *Temple* is a word for Synagogue used by Reform and other liberal denominations, with the notion that they act as replacements for the destroyed temple in Jerusalem. Orthodox Jews, however, will often use the traditional Yiddish terms *shul* or *shil*. To quote the [Jewish English Lexicon](https://jel.jewish-languages.org/welcome) website:

> 
> When Jews use words from this list within their English speech or
> writing, they indicate not only that they are Jewish but also that
> they are a certain type of Jew. Some are Yiddish lovers, some are
> engaged in religious life and learning, some have a strong connection
> to Israel, some have Sephardi heritage, and some are all of the above.
> Because Jewish and non-Jewish social networks overlap, these words are
> not used exclusively by Jews. Some are English words that certain Jews
> use in distinctive ways, and some are Yiddish-origin words that have
> become part of the English language.
> 
> 
> 

The usage of HAY terms in English speech tends to be restricted to Jewish circles, while in secular communcation these terms are not used. It is is therefore an instance of [code-switching](https://en.wikipedia.org/wiki/Code-switching). For more information on Jewish modes of English, see the chapter "Jewish English" by Benor, in the [Handbook of Jewish Languages](https://books.google.co.il/books?id=3IJ1DwAAQBAJ).
Maybe similar to the reason Christians use the Hebrew words amen, hallelujah, hosanna. It is quicker than explaining them in English. The English terms aren't exactly equivalent.