In the comments under Stéphane's answer to [this question](https://french.stackexchange.com/questions/3099/when-to-use-afin-de-afin-que/3100?noredirect=1#comment33294_3100), he mentioned the expressions "de manière que" and "de manière à ce que," as well as "de façon que" and "de façon à ce que."

I'm not clear what the difference is between the version that has *à ce* and the version that does not, for each of those two pairs.