In English it implies it’s a geographical region rather than a nation’s name. The exceptions are for nations that have an adjectival element. The United States, The Democratic Republic of Wherever, etc.
It’s petty semantics that passes by most, but the people that translate Russian official statements in English are aware of the difference and made a point of it for decades specifically to attack Ukraine’s standing in America and the Commonwealth.
Generally speaking, it’s a minor enough distinction that no one would care if Russia didn’t.