"... how one would distinguish between operations research engineer / scientist / analyst / ... outside of my bubble. Hence the question: how would you see the differences between these roles, and are there even any?".
Two ways to distinguish between the naming of the position is by the name of the course in a post-secondary institutions and at an employer.
Employers who ask for qualifications that are not taught in school are also seldom willing to pay for them.
Positions not correctly named are usually open to great variance as to what is entailed, and resulting pay.
It's best to either establish in writing what is required or avoid employers who don't know what they want and the usual amount to be paid.
The name of the position, pay, responsibilities and years in school required are one set of distinguishing requirements, another way to look at it is from the viewpoint of supply and demand.
- You wouldn't want to spend many years in school studying extremely technical material to do a job that has many responsibilities, paid little, and was difficult to find.
- I guess it's ideal if the study isn't too lengthy or mindbending, few people take the course, the jobs are plentiful, and the responsibilities are enough to provide some challenges, but it pays well.
One source of job descriptions and average pay is online job sites, for example: GlassDoor and BetterTeam - Operations Research Analyst Job Description Template.
Operations Research Scientist Salaries in Canada: \$79,471/yr (Average Base Pay, out of 1,414 salaries)
Operations Research Engineer Canada \$71,590
Operations Research Analyst Canada \$58,001
When you look up the average pay in the USA it's much higher, worth moving. Source: ZipRecruiter:
- Operations Research Analyst USA \$88,674/yr
- Operations Research Engineer USA \$162,999/yr
A less biased source of information is probably the US Bureau of Labor Statistics. Clicking on related jobs (with lesser requirements and greater pay) we find: Computer and Information Research Scientists - Masters, \$131,490/yr or Data Scientist - Bachelor, \$100,910/yr.
Future outlook is another consideration, while not related to your question it's useful to consider the future before undertaking the course or planning an employment career.
Some careers are quite safe as far as longevity is concerned, others are either being phased out or have such rapidly changing requirements that your paper is outdated before the ink can dry.