A public blockchain is a permanent, searchable record of who paid whom. Privacy coins treat that as the bug rather than the feature, and use cryptography to conceal amounts, participants, or both.
The approaches differ in a way that matters for how strong the guarantee is. Some chains make confidentiality the default for every transaction; others make it optional, and an optional privacy set is a much smaller one to hide in.
This is also the category where the regulatory question is not abstract. Exchange delistings in several jurisdictions have repeatedly moved these prices more than anything technical, which makes them a recurring subject in regulation markets.