It kind of depends.
As far as a computer is concerned it’s typically two different things. 0 can be a number, or there can be nothing.
The most obvious example is in excel. You can have an empty cell. Make a formula referencing that cell trying to add it and it wl treat it as 0, make one looking for text and it will treat it as “” (blank). But that’s only because excel knows this nuance, try and get more complicated formulas that reference different formulas and it will very quickly through an error at you because it doesn’t know what it’s looking at.
Outside of programming/computers I can’t think of an example where it would matter outside of a philosophical debate
There is a small arguement that saying 0 in a scientific sense implies some kind of accuracy: generally it would be 0.0 implying that there can’t be more than 0.04. but if you say “nothing” that means absolute 0.
That’s a very niche scenario though.
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