That must be it. I incorporated my dad's company as a sole-proprietor and it was dirt cheap. I am guessing the process gets complicated when more than one founder is involved. Blood thirsty lawyers!
I think in BC you don't even need to register if you use your own name, so it's completely free (money/bureaucracy).
The more general term is "register", which applies to the three forms of business: sole-proprietorships, partnerships, and corporations.
What you're thinking of is a business name registration. If you do business as your exact name, you don't need to register a name. If you make more than, $30k (I think), then you do need to register for a GST number.