Codidact runs on QPixel
More specifically, the Codidact project originally had no actual software, and the referenced discord message was a poll deciding whether to create a new, custom Q&A software (the original "Core" project), or to improve upon an existing software (named QPixel) to launch. Ultimately, (as you can tell), QPixel won (due to nobody working on the "Core" version), and so is is currently what powers this site.
It is also worth noting that people other than Codidact are running their own QPixel instances. In fact, much of the point of setting up the Collab site in the first place was to provide a place for questions about setting up your own QPixel instance.
Although all the above technically means that the two are different, the terms (especially when qualified by something like "platform", "engine" or "software") are used more or less used interchangeably unless it's actually necessary to differentiate. Since QPixel is managed by the Codidact Foundation, "Codidact's engine" is QPixel.
The description of this category reads
General Q&A about contributing to or setting up the Codidact (QPixel) platform.
Also, from the official Collab welcome post
This is a special community outside the general Codidact network. Unlike the other topical communities, this one is for questions about the Codidact engine (QPixel) itself.
So, if you have any questions regarding (for example, but not limited to) ...
- setting up a QPixel dev server,
- hosting your own QPixel instance,
- modifying/extending the QPixel software for your purposes, or
- making contributions to QPixel,