The closest equivalent of "area" is "obszar". I think area has too many meanings, including for example penalty area (penalty box) in football - so it can be something really small, that couldn't possibly be called region. If English has exactly the very same (in writing) word as Polish, why complicate it? ;)
Well, if in some translations we're offered both "neighbourhood", then it's pretty much comparable to "area man". And "why complicate" isn't really an argument in a system that slams giant "WRONG!" in your face whenever you pick a synonym it doesn't recognize.
A similar question: why not "district"? Has REGION in Polish a specialised meaning, like "precinct" or "prefecture"?
That's the case, that 'region' is very vague, and 'district' is too specific, too narrowed down. A "district" of a city is "dzielnica".
Polish Wiktionary translates 'precinct' as 'dzielnica' or 'rejon', with the mention that it's e.g. 'rejon komisariatu', so the area on which a given police department has authority
And 'prefecture' is 'prefektura', but my only association with this word is geography of Japan.
They work in this region, "the region" is non specific, the region of what?
What is the difference in this region or the region, exacly the same meaning in my English.