Here where I live I know that non-EEA immigrants get issued both an ID (in which it is specified that it is not valid for expatriation inside the EU nor is it valid for travel within the EU if used alone) and a residence permit/PR, and they need to show both when asked, but I don't know whether there are countries that issue to non-EEA immigrants a residence permit/PR only and identify them only by that. Here where I live they ask both ID and residence permit.
Do EEA countries differ in that regard?
Also, an EEA national has almost no need of any additional paper other than his native country's ID card in order to live, engage, and be indentified in any of the EEA countries I guess (maybe Switzerland is an exception on some minor issues, nevertheless Swiss citizens are treated the same as EU citizens in any other EU country, atleast I think)
But in case this EEA citizen wants to get both an eventual other ID issued by his host country in its format and a residence permit (in case he's in a country that issues both documents to general immigrants), can he get issued such documents?
For the sake of example, can a Dutch citizen living in Germany ask to be issued an ID card in the German format and a residence permit/PR, even if he does not need them and in case he wants them?