I've just never encountered a situation where that's a necessary distinction. If I say "the painting takes up too much space on the wall" I don't need to say "the painting has too much positive space" nor "the painting removes too much negative space".
Just last week I was hanging photos with my wife in our home and after she had proposed a placement I told her "I don't like the balance of the negative space there". I could have said "I don't feel like the parts of the wall not taken up by photos are balanced there" but "negative space" is a convenient abstraction. (Note that this is different from the photos themselves being unbalanced, which is also a concern but was not a problem then.)
Think of it like a foreach loop. Sure, it's equivalent to the corresponding for(;;)-style loop but it's also a convenient mental shortcut.
If you are doing visual design, if you want to call out the parts of the space you are working in where you _aren't doing anything_, that is the 'negative space'.
If you are producing a letterform, all the parts of the object you are producing which is not filled by letter is the 'negative space'. The "space" is the whole area, including the letter.
People intentionally play with the distinction in optical illusions:
https://inthewhitespace.com/2021/11/17/what-it-means-to-be-i...
I think there is a very large difference between saying, e.g., "there is too much space" (the total area is too large) vs "there is too much negative space" (there are not enough things in the area). I think there's a better argument that "negative space" is redundant with "empty space", but personally I don't mind the term so I will not make that argument.
Henry Moore is a sculptor that uses the negative space a lot. It can be useful to refer to the "holes" in the sculpture
https://www.tate.org.uk/art/research-publications/henry-moor...
I think this is a good example of the specific, limited way in which this phrase is useful. It's similar to the - very specific - phrase "price point", which people often use to just mean generic "price" now when they want to sound businessy.