Is it possible to get a bachelor in business administration and then my Master in healthcare management? Or is that not how it works with degrees?

That possible, but different masters programmes have different target groups. This course is open to business graduates, for example: https://www.uni-greifswald.de/studium/vor-dem-studium/studienangebot/studienfaecher/h/hcm-master/

What is my degree was International Management or Business Management? Or is it the same case still?

I'm not going to read that page for you.