Yes and no. I don't think that is entirely true. The key difference as far as I can tell is the American history of slavery which caused Americans to racialize diversity.
In Europe, Africa and elsewhere diversity is expressed in terms of cultural identity, language and customs.
In the American mind, there is no diversity if you don't see variation in skin color. And that is perhaps because there is very little cultural diversity in America. You travel around the US, and every city is kind of the same cookie cutter grid pattern, with the same chains, fast food joints etc.
You go into a Wallmart in Grand Forks North Dakota, or into a Wall Mart on Honolulu, Hawaii and the aisles are exactly the same. People even speak almost the same.
And in Africa you have quite a lot of diversity from the fact that nation states arrived very late, hence tribial identity had not yet disappeared.
Look at at place like South Africa and all the variation you find there. Khoisan, Zulu, Cape coloreds, Banthu, Afrikaaner, Anglo whites and many more.
South Africans don't speak about race and diversity different from Americans because they lack diversity. They do it differently because their history and founding is entirely different.