The Residence Act in Germany regulates the conditions of the residence of migrants in Germany. Citizens of some countries, e.g. Ukraine, are allowed to remain in Germany and the EU for 90 days without a visa. After this period, you need a residence title, which you have to apply for.
Displaced persons from Ukraine have been granted a simplified process pursuant to the mass influx directive [2001/55/EG]: they enjoy special protection in the EU. In Germany, displaced persons receive a residence permit in accordance with section 24 of the Residence Act (AufenthG). From 01/06/2022, this provides access to basic security benefits pursuant to Social Code II.
Further information can be found here:
https://www.gesetze-im-internet.de/aufenthg_2004/__24.html
(Residence Act in full: https://www.gesetze-im-internet.de/aufenthg_2004/)