Yup.
The hweird logical-fallacy use of "begging the question" is a mistranslation.
It goes back to Aristotle, who talked about "τὸ ἐξ ἀρχῆς", meaning "asking for the first thing". That is: you're debating some proposition X, which in the rhetorical terminology of the time was called "the first thing" (imagine that you're holding an actual debate, and you start by saying: The question before us is whether X), and the logical fallacy is when, in the course of arguing for X, you assume (ask us to accept -- ask for) X, the "first thing".
So far, so good.
So after the age when Serious Thinking was done in Greek came the age when Serious Thinking was done in Latin. Aristotle's term was translated to "petitio principii". The first word means "assuming" in mediaeval Latin but "asking for" in classical Latin. The second word means "first thing", a rather literal translation of the Greek.
So far, still so good.
And then, some time in the 16th century, some genius decided to translate the term into English and (1) render "petitio" as "asking for" ("begging") rather than "assuming", and (2) render "principii" as "question" instead of "first thing". Presumably they did #1 because "asking for" is one meaning of "petitio", even though it's not the one that's relevant here. Presumably they did #2 because in a debate (which, again, was the original context for the term) "the question" means whatever proposition you're debating.
The result of which is the ridiculous term we have now. The common usage of the phrase to mean "raising the question" is a much better thing for "begging the question" to mean. Personally, I mostly avoid using the term at all because some people will think it means "raising the question" and think I'm weird and pedantic if I use it to mean "arguing in a circle", while other people will think it means "arguing in a circle" and think I'm ignorant if I use it to mean "raising the question". (So it's an example of what Fowler called a "skunked" term: https://en.wikipedia.org/wiki/Skunked_term.)