All these job titles don't really have a formal definition. Software engineer = programmer = software developer. Computer scientist sure does sound fancy though. There's no committee that will say "actually you're doing too much math to be a developer sorry." We all do the code-y thing. Businesses seem to pick one at random based on seniority. I just call myself whatever my most recent job title was.

Your industry will affect your specialisation and skills much more than anything else.

- Software Engineer (Maths)