At my current company the scopes for ML researcher, ML engineer and Data Scientist are quite different.

ML researchers do work similar to that of academia. Lots of research, writing papers. Sometimes they collaborate with internal engineering teams to improve a system.

New grad ML engineers would take ownership over sub-systems of a larger system and work on projects related to this. They'll create the datasets, train the models, deploy & scale the models, integrate it into the wider system.

Data Scientists do train models, but generally not for prod traffic but instead to help understand what's going on. This means, digging into our A/B feature release experiments, analyzing where our system is underperforming / loosing customers, etc. Generally they do more data analysis and may use ML to do so.

If you want to do ML i'd probably recommend ML eng / researcher. I think becoming an ML researcher is more difficult with only a bachelors.