“statistics” can mean two things: it’s a field of mathematics, and it’s also the application of that field to the real world.

There are many theorems in statistics: the central limit theorem, the proof of the t-test, for example. This is maths.

But if what you’re doing is assuming a certain real distribution is normal, or testing for normality of real data, that’s not maths any more.

Just like calculus is real maths, but once you’re solving real integrals for real scenarios, you’re doing science.