From the case of US, I understand that nationals are not the same as citizens. That is, a person who is allowed to stay permenantly in a place may not receive a passport.
Recently Germany passed a new law on citizenship (as far as I understand), but videos news articles and videos often use imagery of a passport.
So, does this mean that in the case of germany that citizenship means one has to get the passport neccesarily? Then, what happend to the niederlassungserlaubnis?
From the case of US, I understand that nationals are not the same as citizens.
Correct. Under US nationality law, all US citizens are US nationals, but there are some US nationals who are not US citizens.
That is, a person who is allowed to stay permenantly in a place may not receive a passport.
That's also correct, but it doesn't apply to US non-citizen nationals, who are in fact eligible to receive US passports. People who have the right to reside in the US permanently but are not eligible to receive a US passport are for the most part called "lawful permanent residents" or green card holders. (There are some other categories of people who are neither US nationals nor lawful permanent residents, such as the nationals of the freely associated states.)
Recently Germany passed a new law on citizenship (as far as I understand), but videos news articles and videos often use imagery of a passport.
So, does this mean that in the case of germany that citizenship means on has to get the passport neccesarily? Then, what happend to the niederlassungserlaubnis?
If you are a German citizen you cannot get a Niederlassungserlaubnis, just as a US citizen cannot get a green card (nor can a non-citizen national). Someone who naturalizes in Germany becomes eligible for a German passport, but is not required to obtain one. (German citizens are however required to have a valid ID of some sort, so there's a requirement to have either a passport or an ID card -- Personalausweis in German.)
You may be confused because people often use "get [some country's] passport" to mean "obtain the nationality of [that country]." This is a figure of speech that doesn't necessarily reflect administrative details very closely.
The US and German systems are somewhat different as far as the administrative and legal requirements to obtain a green card or Niederlassungserlaubnis, but thet have this in common:
From the case of US, I understand that nationals are not the same as citizens.
That's really US-specific terminology. There are other similar distinctions like the various types of British nationality, each somewhat different from each other.
That is, a person who is allowed to stay permanently in a place may not receive a passport.
As noted in a comment, US nationals can actually get a US passport. As far as I can tell, the main difference is their right to vote in federal elections. None of this readily generalizes to other countries and it's not useful to understand Germany nationality law so I won't elaborate further.
On the other hand, in the US as in Germany, there are people who have the right to reside more-or-less permanently without being citizens. That's not what the nationals/citizens distinction in the US is about and permanent residents do not get US passports. If they need a passport (in Germany it is mandatory, in the US it's not), they would get it from their country of origin. There are also various statuses and passport-like documents for people who cannot do that (refugees, stateless people).
Recently Germany passed a new law on citizenship (as far as I understand), but videos news articles and videos often use imagery of a passport.
That's because becoming a citizen allows you to receive a passport. In Germany, a personal ID card (Personalausweis) is even more common but I guess passport pictures are just easier and, as pointed out in a comment, more distinctive.
So, does this mean that in the case of Germany that citizenship means on has to get the passport necessarily?
Not exactly but German residents do have to hold a government ID (either a passport or a Personalausweis). If you become a German citizen, you often have to relinquish your previous citizenship and will need either of those.
Then, what happend to the Niederlassungserlaubnis?
Nothing, that's completely unrelated. As noted, that's not what the nationals/citizens distinction in the US is about and that's not what the new German law is about. None of this means the permanent resident status has disappeared. This status still exists.
The answers by Relaxed and phoog cover the meaning of Niederlassungserlaubnis, which was the main part of the question. However, there are subtle distinctions between holding a German passport, being a German citizen, and being a German.
As a citizen, you have the right to reside, therefore the permission (Erlaubnis) to reside is no longer required.
A national ID or Passport is taken as proof of this right.
Since a residence permit will be revoked through a change or loss of citizenship (Allgemeine Verwaltungsvorschrift zum Aufenthaltsgesetz 52.1.2), the Niederlassungserlaubnis will no longer be valid.
