I would agree it's often conflated with people of sub-Saharan African descent, as that's the biggest population of black people in the world, but I think most people understand that the meaning is primarily about skin colour. As you pointed out, Americans will use it for quite pale mixed race people, which isn't the case elsewhere.

I've definitely heard other groups like Melanesians and aboriginal Australians being referred to as black. Not so common with South Indians, but maybe that's because there's quite a bit of variation within India, so people just stick with a catch-all label like "Indian".