> I'd argue against most countries not having their own classification system. That has not been my experience, and I don't understand how e.g. a demographic census would even function otherwise.
Many countries collect data on ethnicity-hence, they will have a system for categorising people based on ethnicity, often based on which ethnicities are most common in that country. But the US is unusual in having racial classifications instead of purely ethnic ones.
Differences: race purports to be a biological classification, ethnicity is predominantly a cultural one; racial classifications very often attempt to sort everyone into a small number of categories, while ethnic classifications tend to be much more expansive (with dozens or even hundreds of categories)–e.g. the Australian government's system recognises over 250 distinct "cultural and ethnic groups" [0]
Consider the case of identical twins separated at birth, and raised by families belonging to different ethnic groups-the twins could grow up to have different ethnicities, but few would agree they could have different races. Suppose one twin is adopted by an Italian family and grows up speaking Italian at home, while the other twin is adopted by a Lebanese family and grows up speaking Arabic at home instead
In theory (and occasionally in practice), you can change your ethnicity - sometimes a person joins an ethnic group (often via marriage, religious conversion, and/or immigration), and becomes so thoroughly assimilated to it that everyone accepts them as a full member. A relatively rare scenario-and different ethnic groups differ in their openness to it-but given ethnicity is a cultural category there is nothing in principle wrong with the idea of changing your ethnicity. Whereas, in theory, your race is immutable and cannot be changed (in spite of rare cases when practice has deviated from the theory)
[0] https://www.abs.gov.au/statistics/classifications/australian...