Just in case this stuff was too easy to understand, there is an interesting overlap between what is commercial according to CAR 206 and what is private according to CAR 2(7)(d).
CAR 206 specifies operations requiring an AOC, CAR 2(7)(D) specifies what is permitted with a PPL. (I think...)
It appears that some operations are permitted on a PPL, but require an AOC. The overlaps are certain agricultural operations, aerial spotting, aerial photography etc. I have never been involved in these operations, so I don't know whether this is how it is implemented in practice.