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 Hamburg, there are two types of secondary schools, the district schools and high schools/gymnasium. Another type of school is vocational schools.
District School
The district school covers the grades 5 to 13 and offers all school graduations up to graduation from high school. In the district school all pupils learn together. Children who are weaker in their performance, as well as more capable ones, are specifically supported and demanded. The district school is more focused on the acquisition of competences for the design of the professional lifepath (vocational and study orientation).
http://www.hamburg.de/stadtteilschule/2670728/stadtteilschule/
Grammar School
The grammar school covers the grades 5 to 12. It teaches pupils with the goal to lead them after grade 12 to the general university entrance qualification. The general grammar schools offer high-performance pupils not only subject teaching but also interdisciplinary teaching, opportunities for specialization in terms of performance and inclination through numerous choices in languages, natural sciences and the aesthetic disciplines and support for particularly gifted pupils (promotion of excellence).
At grammar school all school graduations can be made.
http://www.hamburg.de/gymnasium/
Vocational schools
At VET schools, young people have diverse possibilities to earn higher school graduations. This can be done before, during or after vocational training as well as in other specialized educational programs.
Higher Commercial Schools or Higher Technical School: Young people develop their professional skills and finish after the 12th grade with the University of Applied Sciences entrance qualification.
The Vocational High School (in the fields of economics, technology, education and psychology) leads in a three-year course to the Abitur.
As part of a dual vocational training, young people can acquire the university of applied science entrance qualification with additional lessons at the vocational school (Dual plus university of applied science entrance qualification). This is also possible at many fully qualified vocational college schools.
At "Fachoberschulen" or "Berufsoberschulen", young people who already have completed a vocational training can acquire the university of applied science entrance qualification or the general university entrance qualification.
In continuing vocational trainings young people can obtain the university of applied science entrance qualification as well at technical colleges.
https://hibb.hamburg.de/bildungsangebote/hoehere-bildungsabschluesse/