Comparing career trajectory between getting MSc vs MASc degrees in similar fields

As an applicant, I noticed that some Master of Science (MSc) and Master of Applied Science (MASc) programs have faculty conducting similar research within my area of interest. These programs can be divided into engineering faculties and science/medicine faculties.

I'm worried that graduate studies at an Engineering Faculty will pigeonhole my academic career options by restricting me into only conducting research at an Engineering Faculty. I don't have an engineering background, but I looked at MASc programs because I liked some of the potential supervisors.

Thank you!