An overview of the school system in the federal state of Berlin can be found at: https://www.berlin.de/sen/bildung/schule/bildungswege/
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 (https://www.berliner-privatschulen.de/).
After primary school, there are from grade 7 onwards three types of general education school and there are vocational schools.
Integrated Secondary School (ISS)
In Integrated Secondary School, high-performance and under-performing students receive individual support. There are offers at different levels. In the Integrated Secondary School, the following qualifications can be obtained after passing the examinations: Basic Vocational Education Maturity at the end of the 9th or 10th grade, Advanced Vocational Education Maturity and Middle Maturity after grade 10 and General University Entrance Qualification after 13th grade.
https://www.berlin.de/sen/bildung/schule/bildungswege/integrierte-sekundarschule/
Community School
In the community school, the longer common and individual learning from class 1 to 10 and even to class 13 is firmly anchored. Community schools without their own elementary school or without their own upper level have binding cooperation with elementary schools or upper levels from other schools. Pupils at a community school automatically change to grade 7 at their school if they want it. Likewise, pupils from primary schools with whom compulsory cooperation exist will be given priority. Like the integrated secondary schools, the community schools lead to all school qualifications (https://www.berlin.de/sen/bildung/schule/bildungswege/gemeinschaftsschule/).
Grammar School /Gymnasium
The Gymnasium covers the grades 7 to 12. It provides a deepened general education and includes the education to obtain the general higher education entrance qualification (Abitur) after class 12. Usually, the Gymnasium begins with the 7th grade. Around 30 Berlin grammar schools start already with the 5th grade and are aimed at children with special talents (https://www.berlin.de/sen/bildung/schule/bildungswege/gymnasium/).
Information about the vocational schools you will find in the age group 16-18.