It gets even more complicated later on, as explained by Crap My Kids Watch:
In later seasons, stories are introduced by his cat (in puppet form for some reason), who apparently can talk, but only in puppet form. In the story that the cat has introduced, the not-grandmother is still narrating, and the cat is now Caillou’s not-special, not-talking, not-puppet cat. I don’t get it at all.
Source link LOL