The federal states are responsible for education policy in Germany. They have the so-called cultural sovereignty, so that the state governments can largely independently decide how they organize their education systems. Therefore, the terms for the types of schools in general education are very different. Further information is also available on the website of the Conference of Ministers of Education: https://www.kmk.org/themen/allgemeinbildende-schulen/bildungsweun-und-abschluesse.html
State of Rheinland-Pfalz
Information about the school system in Rheinland-Pfalz, also in different languages can be found here: https://bm.rlp.de/de/service/publikationen/?tx_rlppublications_list%5Btopic%5D=54&tx_rlppublications_list%5Baction%5D=list&tx_rlppublications_list%5Bcontroller%5D=Publication
There are state schools in the majority. Some schools are in ecclesiastical sponsorship but awarded the state-recognized degrees. There are some private schools that charge different levels of school fees.
In Rheinland-Pfalz, the choice of secondary school takes place already after the fourth grade, as a rule, the children are at the age of about 10 years old. You will find the information in the age group 6 to 12.
At the age of 12, a change of school will take place only if the child is unable to cope with the chosen school.