The sites Help page incorrectly calls out for italic and bold. These should be replaced with the proper emphasis and strong definitions respectively. As while these are usually rendered as currently described, that is not necessarily the case, and is inconstant with elsewhere in the specification documentation. This may also be what results in many of the “why no underline or how to underline” questions, as people are expecting these to be visual styles, and not contextual ones.
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I couldn’t agree more, *Italic* and **Bold** should never have been used in the quick reference and tutorial when these words are not part of the spec. I opened a Github issue about this in October 2023.
At the very least, I would change the help page and tutorial to use “emphasis” and “strong emphasis” to match the current spec ASAP.
But I would also consider updating the both the spec and website to use the modern terminology “stress emphasis” and “strong importance”. Treating this syntax as equivalent to <em> and <strong> HTML elements while still calling them by their former names not only makes the CommonMark spec less clear, it also teaches obsolete HTML semantics to novices.
A PR with the suggested changes would take less time and have a greater chance of effecting change than this discussion 
You don’t even need to clone the repo or run tests, and you can do it via the GitHub web interface.