The reason they don't explain how it works is that the CSAM hash matching is an algorithm from NCMEC, which was apparently originally designed by Microsoft.
If you want to learn about the algorithm/hashes, you have to, among other things, sign an NDA about it, so it's likely that Apple, legally, cannot go into detail about how it actually works.
crosschecking hashes is only possible if they use the „same“ implemantation for the hashes. it would be safe to assume that the implementation/algorythm is the same regardless of being called photodna/neuralhash.
If you want to learn about the algorithm/hashes, you have to, among other things, sign an NDA about it, so it's likely that Apple, legally, cannot go into detail about how it actually works.
Microsoft has a page on it here if you're interested: https://www.microsoft.com/en-us/photodna
For obvious reasons, they don't go into a whole lot of detail.
I've learned a lot about how the process works from this blog post: https://hackerfactor.com/blog/index.php?/archives/929-One-Ba...
He gets a few facts about Apple's approach wrong, but it's an incredibly interesting read.