It is the same thing in Canada. "Engineer" is a protected term so that people can trust that when someone calls themselves an engineer, or does "engineering work", offering services to the public, they can trust that means something.
One difference is that the profession is 'Self Regulating', meaning Professional Engineers Ontario is a non-governmental body made up of Professional Engineers that is trusted by the government to manage the profession. The Quebec version of this organization, Ordre des ingénieurs du Québec, was put under "trusteeship of the provincial government" when the government lost that trust after some infrastructure accidents [0].
The question of what constitutes "engineering work" is well defined in the Professional Engineers Act (Ontario) and would probably cover a lot of what you mentioned as 'science, math, software' not having licensing. So according to Professional Engineers Ontario, some of the types of work that those types of people could produce could require the sign-off of a Professional Engineer if it falls under the definition of "engineering work" by the PEO:
[1] Under the Professional Engineers Act, the “practice of professional engineering” means “any act of planning, designing, composing, evaluating, advising, reporting, directing or supervising that requires the application of engineering principles and concerns the safeguarding of life, health, property, economic interests, the public welfare or the environment, or the managing of any such act”.
To determine whether you are practising professional engineering, ask yourself three questions:
Are you planning, designing, composing, evaluating, advising, reporting, directing or supervising, or managing any of these acts?
Are engineering principles required to carry out the act?
Does the act concern the safeguarding of life, health, property, economic interests, the public welfare or the environment?
As a licensed engineer in Ontario, I'm to display my licence at my place of work. I also keep another image close by to make sure we all remember not to take ourselves too seriously.
https://imgur.com/Rd3XFyy
[0] http://www.cbc.ca/news/canada/montreal/quebec-engineers-regu...
[1] http://www.peo.on.ca/index.php?ci_id=1848&la_id=1