In Canada anyway, a software engineer is someone who actually did an engineering specific bachelor program. All engineering degrees must have gone through the same common classes for math, physics, chemistry, etc. Plus the major specific classes. It really focuses on the engineering aspect, like in construction or mechanical engineering.

And you can't call yourself or call a job/role "engineer" unless you are a part of an order of engineers of your respected province. It's highly regulated.

In the US, anyone can call themselves engineers.