The difference is that zero is explicitly a number, rather than a concept. Making it a number allows it interact with the rest of mathematics in a consistent w

The difference is that zero is explicitly a number, rather than a concept. Making it a number allows it interact with the rest of mathematics in a consistent way, which I'd argue you can't do with "nothing". To use your later example of "no apples": Is no apples the same thing as no bananas? What about no meters? I honestly don't know, the question is a bad one. My gut says yes, nothing in each case is just nothing. Is zero apples the same thing as zero bananas or zero meters? No, they're different because the unit "apple" is orthogonal to the unit "meter". The precision of zero is what's so special about it.