Right, probably a similar meaning then.
My guess is that Hindustan is an endonym in the Central Asian languages. The reason those people in those countries call India “Hindustan” is because they’ve had contact with India for hundreds of years. As where the name for the United States is probably an exonym in their languages, since they didn’t have contact with Americans before last hundred years of so probably. Plus, those languages were highly “Russified” during Russian and Soviet rule. The Soviets even made attempts at killing those languages (you kill a language, you kill a lot of that culture. If someone’s not connected to their identity as a Kazakh, then they can easily become a Soviet culturally.)
I don’t think I quite used endonym/exonym right in this context, but what I’m trying to say is that “Hindustan” is the traditional, historical name for India in those languages. It’s most likely always been the name in those languages, so there wouldn’t be a need/point to changing the name. As where, those languages never had a name for the United States, so instead coming up with a name in the traditional style, they most likely just burrowed a name from the Russian language or just used a name that sounded similar to the English version.
I’m sure you didn’t need, nor want, all this explanation/theory, but I have a tiny, little interest in language, culture, and communication