from my limited knowledge the difference between them is basically the shape of the mouth, one is designed for browsing (the Black) and the other designed for chomping/grazing (the White) and thus what they feed on. the Black eats foliage off of low bushes and trees and grass while the White eats grasses.
What do rhinos eat? | Reference.com
In fact, from my research, the White is a mistranslation of the foreign word which should have been translated as "wide".
The other difference we were told and I cannot remember what species does what, is that one species the young precede the adult when fleeing and the other the young trail the adult.
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here is a cropped photo of the mother cheetah and cub we found in the Serengeti National Park in Tanzania. The Thompson's gazelle they are feeding on would be on the lower right of the photo if uncropped. You can really see how the long grey/black guard hairs on the cub would enable it to disappear if it crouched down and remained still.
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my wife, Judy, grabbed this shot of the adult giraffe feeding, the adolescent looking at us and the impala ignoring everything at the Lake Manyara National Park