Does anyone know the origins of the similar Jewish surnames Rappaport and Portnoy, probably from Poland or Russia?

Well, there's a claim that Rappaport/Rappoport is a Italian-Jewish name of Mantua, with roots in Germany and branches in Poland. The etymology and history seem vaguely dubious to me, but see what you think of the site below. Portnoy sounds like a French version of something eastern European. Let me see what I can do.
https://en.wikipedia.org/wiki/Rappoport

I've run into a few claims that "portnoy" means "tailor" in Russian. Since Russian is not one of my languages, I can't confirm this, but here's one site:
http://www.languagehat.com/archives/000416.php

From Chat Board:

"What I found fascinating about Jewish last names is that both Schneider (German, which I don't know, for tailor) and Portnoy (Russian, of which I know some, is also tailor)are both comon Jewish last names."

https://familysearch.org/wiki/en/Jewish_Names_Personal

Schneider (German/Yiddish), Kravitz (Polish) and Portnoy (Russian) all mean tailor. (satguru)

Rappaport and Portnoy are not actually related etymologically. The Rappaports are a large branch of a family related to priests (Cohanim), who share a common ancestor (the high priest Aaron, brother of Moses). Portnoy is Russian for tailor, and could be a translation of the German "Schneider", a name that would date from around the end of the 18th century (when Emperor Franz Josef I of Austria decided that every citizen of his empire must have a last name, and most Jews at the time did not).