I'm Carribean and don't know why African Americans always say the above as though it is right or means anything.I suppose it is ignorance so let me educate.
To be clear, Indians in general are not darker than Africans. Some may be darker than African American but remember that African Americans are mixed race and their skin tone is actually lighter than it was when blacks first came to the Americas. Most blacks on Earth are black or close in skin tone to original black Americans. So just at base, you're wrong about skin tone difference. A Tanzania has darker
To address a wider point, skin color or not, blacks are a different race to Indians. My Carribean country has Indians and they have more aquiline noses, straight hair, smaller bodies, different skin thickness, different athleticism, skin glamor, different culture, different predispositions etc. They are, in short, like cacs except not as impressive or imposing (lol). African Americans don't do know it but there are many loci on which a people may think themselves superior to another. Skin color is but one of those loci.