Well, the correct standard, in fact.
IEC 62304 is not a product standard, it's a process standard. For example, for embedded software in medical electrical equipment, the "product" standard is IEC 60601, which is the medical electrical equipment product safety standard - and is does include software requirements, including "calling" IEC 62304.
We did not have such a product standard for standalone (SaMD) software, so IEC 82304 was created. Not, it's the "product"safety standard fot this type of device, and it calls IEC 62304 (in the future, it will probably be harmonized with the directives as "the" product safety standard for SaMD).
Since standards are not mandatory, and our NB has not said anything about it, that can't we just keep using 62304?
First, because it's the correct way to apply standards. If you are simply trying to do something to pass the audit, instead of what is correct, my experience is that you will have a lot of trouble in the future (this is a general problem that most manufacturers have nowadays, unfortunately).
Second, and it related to the first, is the way you approach product compliance. You can approach is in a reactive way (again, only doing what you seem is enough NOW to get an approval), or you can do it in a strategic way, which includes an understanding that the expectations changing and that it's better to do more/ the right thing now because it will save costs in the future.
For example, as I mentioned, IEC 82304 was created to be the product safety standard for SaMD. It will probably be harmonized in the future (and even if it is not harmonized, it will still be the product safety standard for SaMD, anyway). If, in the future, you re expected dot how compliance to it, you will probably have some trouble (this already happened with IEC 62304 because it was harmonized and people did not use good software engineering to design medical device software and then it was impossible to fulfill the requirements of the standard, which applies to medical device software design. We even had to create an solution to "legacy"software in the Amendment).