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Explanation: There is no one definitive version, but all I can talk about is what I think is becoming most common. I spent a good few years as editor of a business magazine about Russia and we settled on these as the best definitions.
I have no objection about using oblast in transliterated form, as long as you know that the target reader has a base of knowledge about how Russia works.
But generally we would talk about Moscow Region as opposed to the City of Moscow. Leningrad Region rather than St. Petersburg etc.
I assure you, in the UK at least, region is more contemporary and common than province.
But that leaves the question: how can you translate rayon if oblast is a region!
A rayon is normally either a sub-division of an oblast or an urban sub-division. In each case, the most natural translation is district.