I didn't say that things were different from the EU directive, I said you have to check the things which are specific to each country in national law. You can't tell from anything in that text if Spain requires registration or not or how one goes about registering. Hope that's clear.

I think you are correct. A EU regulation has binding force in each member state directly. There is no difference in each member state. Directives on the other hand lay done certain results that need to be achieved by the member states. The directive also needs to be transposed into national law to be binding. So in case of directives it is better to search for the national law and read that.

Well, in post #13, that is exactly what you said, "but clearly there are things specific to each country". And never provided fact to back up such opinion.
National laws are just copy & paste of EU Directives. I will always look at europe.eu archives for up to date info, better organized then national archives of random states.

So what does "may" mean? To me it indicates a choice for the member states. A member state may require EU citizens to register or they may not. You cannot copy and paste such a clause into national law. The member states have to make a choice here. They will need to address the right national authorities to implement such a choice. Copying that clause from the directive will only lead to total confusion and legal uncertainty. That is not how to run a country based on the rule of law. So, no, national laws are not simple copies of EU directives.

In that text, it does not specify well known differences between Ireland (no registration at all required before 5 years), France (optional registration at the town hall for a carte de sejour), Netherlands (registration after four months), Spain (registration before 90 days) anywhere. Point it out to me if I'm wrong.

Regulations like GPDR are passed into national law as a single Act/Reglamiento with minimal changes to the text. Directives like the 2004 FoM directive on the other hand need transposing into national law, they are not a simple copy and paste job. Directives require "member states to achieve particular goals without dictating how the member states achieve those goals" (Wikipedia) so you do have to check the member state's national law.