Statistics has a sort of funny and peculiar relationship with mathematics. In a lot of university departments, they’re lumped together and you have a “Department of Mathematics and Statistics”. Other times, it’s grouped as a branch in applied math. Pure mathematicians tend to either think of it as an application of probability theory, or dislike it because it’s “not rigorous enough”.
After having studied both, I feel it’s misleading to say that statistics is a branch of math. Rather, statistics is a separate discipline that uses math, but differs in fundamental ways from other branches of math, like combinatorics or differential equations or group theory. Statistics is the study of uncertainty, and this uncertainty permeates the subject so much that mathematics and statistics are fundamentally different modes of thinking.