What kind of different careers would a Masters in Statistics, Operations Research, or Analytics offer me?
Many?
The most obvious for a statistics degree would be as a statistician. Statisticians work in many settings, though - your work could be as diverse as doing biostatistics for a hospital or academic medical center to modeling financial data for an insurance company or bank. Statisticians also work at think tanks and nonprofits doing more social science research. It just depends on what you want. It’s a versatile degree.
Operations researchers help businesses run more efficiently (an oversimplification, but useful). So an MS in OR would probably have you working for a corporation helping them improve processes, and most corporations that can afford that kind of thing would probably be large for-profit ones. Some ORs may also work as consultants to help businesses strategize for mergers, acquisitions, streamlining, etc. But because of the strong quantitative skills of ORs, there are lots of quant careers that could be open to you if you want to change careers.
Analytics is more difficult because the quality of analytics programs varies and different things are called “analytics” or “analyst.” Some analytics programs have strong statistics and CS components and prepare people for careers as statisticians or data scientists, but with more business training than the average stats program. Other analytics programs are really business master’s, but with some more stats (and maybe CS) thrown in - they’re more for people who are managing analysts or doing light analytical work but won’t prepare you for a real analytical role. I’ve even seen a few analytics master’s that seem more for people who desire an IT career or something.