As a PhD mathematician, I’ve always guessed that 9 is smaller than 8, but not less than 8. So I did too. Why?

What is technically correct terminology if there is unspecified context to it? If you are talking about integer numbers then I would prefer to say that -9 is lower than -8. If you are talking about the magnitude of the numbers, rather than their place on the integer number line, then -8 is smaller and lower than -9 (although I would prefer to say smaller). As there is no technically correct answer to the questions, these phrases are often used interchangeably in practice. What is mathematical notation like 9?

“Less than” is another good alternative phrase. It is the words intended by the sign of the letters.

I would say that a small number is close to 0 and, in a context where negative numbers make sense, a low number is close to minus infinity. The simplest way to explain a business number is to give an example.