Hello

Both are good, depends on what you want to work on. Since you are a biomedical engineer so you may plan to go into a hospital where your skills would be relevant.

Simply said, Hospital management has a focus on Hospital and its departments, health management has a focus on overall health aspects and programmes which may include hospitals too.

As far as exams go it depends on specific college but in India you can give SNAP for symbiosis, TISS has its own exam, CAT, MAT and even GMAT for all other colleges.