Waitlist usually turns to rejection. It is likely that UCB will use the waitlist less this year, since some full-pay students who would otherwise choose more expensive private universities will choose the less expensive in-state public. In any case, matriculate to Yale (assuming you prefer it over UCLA, since you did not mention UCLA before) so that you have a place to go to college next fall. You can still consider the possibility of a waitlist admission from UCB so that you know what to do if it happens, but don’t get your hopes up too high.
UCB does have about twice as many pure math majors as Yale. But it also has a much larger number of applied math majors than pure math majors (unlike Yale), so that may affect the “flavor” of the math undergraduate community there.
Beyond that, UCB will likely have a more “economy class” feel, while Yale will likely have a more “luxury class” feel, even though the math courses and research will be high quality (in terms of content, rigor, etc.) at both.
Note that Yale has a foreign language graduation requirement: https://yalecollege.yale.edu/sites/default/files/2019-09/FL-chart-2016%5B1%5D%20%281%29.pdf . As a pure math major, you may want to consider choosing French, German, and/or Russian as a foreign language to study, since math research papers may be written in these languages, and a reading knowledge of one of these languages is a common math PhD program requirement.