IANAL, but 99% sure that the situation in Germany is that you have to identify yourself (give name, birthday, (address?)), but you /don‘t/ have to carry (or show) your government issued ID at all times.
You don't have to carry it, no. But if you don't carry your ID (or equivalent) and they have a reason to ask for it (e.g. you are a suspect of a crime), they can require you to take them wherever you keep your ID or to the station.
I figured it worked the same in the Netherlands, but from what I can tell it's true that you always need to carry it and you can get fined if you don't. So quite a bit more strict. That sucks.
I actually recently asked a German police person the exact same question if I have to have my ID/passport with me at all times.
The answer was “no, you just need to own one or the other”.
I always thought as well that there is “Ausweispflicht” (ID carrying obligatory) in Germany.
I figured it worked the same in the Netherlands, but from what I can tell it's true that you always need to carry it and you can get fined if you don't. So quite a bit more strict. That sucks.
https://de.m.wikibooks.org/wiki/Rechte_und_Pflichten_im_Umga... (German)