If you live in Germany and work in the Netherlands, you must also pay your taxes and social security contributions in the Netherlands. (Attention: there are exceptions).
As a resident of Germany, you also have certain rights in Germany. For example, you remain with your own health insurance and you can continue to see your family doctor in Germany. If you become unemployed, you apply for an unemployment benefit in Germany. In the Netherlands, the pension system is different. Not worse than in Germany, but organised differently.
You can find general information about the social security system in the Netherlands in the brochure from the Deutschen Rentenversicherung [German Pension Insurance]:My Time in the Netherlands – Work and Pension Europe-wide.
General information
Burgerservicenummer [Citizen Service Number] (BSN)
DigiD
A DigiD is an online login tool linked to your Burger Service Number. With a DigiD, you can do things online, for example with the Tax and Customs Administration, the SVB, the UWV, other government agencies, health insurance companies or pension funds. In the digital environment, you can then read news, make applications, file tax returns and so on.
Even if you live in Germany, you can use the Dutch DigiD. If you do not yet have a DigiD, you can easily apply for one, even if you do not have Dutch nationality. You can find more information about this on the Nederland Wereldwijd website (only in Dutch).
You can read how to apply for the DigiD here (in Dutch or English): Digid.nl
When you apply for the Dutch DigiD from abroad, you will receive a code for a DigiD switch. With this code, you can get the activation code for the DigiD in a video call with 24/7 Nederland Wereldwijd. You will then no longer need to go to a DigiD counter.
Residence / work permit
If you do not have EU nationality, your employer in the Netherlands often has to apply for an employment permit (TWV). Whether you also need a residence permit (possibly in combination with a TWV) depends on your nationality, place of residence and work. You can find more information about this on the IND website (the website is available in Dutch and English).
I lost my job five years ago. I went straight to the Netherlands to see if I could find a job there. In Germany I didn´t find a job that fitted my profile. Now I have almost the same job as before in Germany and earn even more. In the beginning, I had to get used to the different regulations for cross-border workers. But if you ask me, that´s the only disadvantage: a lot of extra paperwork! The GrenzInfoPunkt explained all the things I have to pay attention to.