What I've found by following Wakabayashi Toshiya for several years, is that he has always called his webcomic Tsuredure Children, back when he first started posting it on his site, every single comiket that he's released doujins containing bonus chapters, he has always referred to it as Tsuredure. I mean, the website he made specifically to post them is http://tsuredurechildren.blog40.fc2.com/
The reason the online chapters no longer match up with the published ones (the first couple volumes match up almost exactly, outside of him redrawing the first several due to his style having changed so much) is because once he got picked up by a publisher, he has to get permission to post the new ones online.
(As an off-topic side note, I've wanted to do his other ongoing series for ages, but it would kill my cleaning staff)