China is a country of multiple ethnicities, some of which can also be found in its neighboring countries, like Russia and Koreas. So the same ethnic groups are named the same as that in such other countries, like 俄罗斯族 and 朝鲜族.

But in the case of a minority ethnic group which is also found in a central Asian country, it is named 乌兹别克 for the country, but 乌孜别克 for the race living in China, why is there the different spelling for the same thing?

P.S.: 壮族in China is named 京族in Vietnam， but there are also 京族 living in Hainan and Guangxi of China.