It depends. Some schools only offer one or the other. A BA at one school may have the same requirements as a BS a another. Others offer both, with a difference in requirements. For example, Yale’s BS requires two semesters of pchem and an additional advanced course of your choosing.
Quite a bit more, and I got my own faculty office and access to the faculty bathroom in the Math building. (This was in Louisiana so the old buildings had two sets of bathrooms, separate but equal. )I taught three different classes - data structures, architecture (using slides from my adviser) and CS 101 for honors students. So I got nothing done on my research that term, but they never bothered me again.
It was annoying because when I came down I specifically negotiated that I wouldn’t have to teach.
The CS 101 class only had like four students in it since the department chair had gotten some woman from his church to teach it before, and the word spread to avoid it.