I'd like a career under something that falls under Genetic Engineering>Genetics

I'm really interested in DNA modification. But I'm kind of confused on what to take in college. I was looking into Genetics>Geneticist and it seemed like it was more medical. I think what I'm looking for falls under more Biotechnology maybe? I'm really confused.

One thing to realize is that there is no career in "-insert research topic here." Rather there are jobs/careers that may (or may not) require knowledge in a certain area. I.e. you do not have a genetic engineer, but e.g. a process manager/analyst/project manager with relevant genetic (or other technical and non-technical) knowledge.

As such it is is wrong to see college as a type of vocationa education but rather as a means to follow ones interest. That being said, the course that are relevant to your interest will vary from school to school. There is always a requirement for basic molecular genetics (regardless of system or application) and then some specialization afterward.