While the two names are different, they both require a medical background, meaning that a lot of the courses in these two majors have a medical background. The former is fairly mechanical + medical, focusing on mechanical and materials, while the latter is biological + medical, focusing more on biology.
If you choose biomedical engineering for graduate school, you can work in pharmaceutical and medical device companies, especially in the medical device industry, which is considered to be a sunrise industry, and the treatment of R&D or sales personnel is good!
I hope to help you yo!