The only limitation to having an engineering degree vs. not is whether or not you can legally call yourself an "engineer". It makes no difference in any other respect - there are *plenty of software engineers in Canada who do the exact same job without the title.
There is no legal prohibition against you performing engineering work - anyone is allowed to engineer (the verb), but not everyone is an engineer (the noun).
There's also no classification difference merely based on what degree you have. The word "professional" AFAIK has no legal meaning, in Canada, in the context you're talking about.
Engineering is considered a professional degree - but that has no bearing on whether or not you're allowed to be hired into an engineering position, or have to join a union, etc etc.