Taxonomy of schools
Educational institutions are often categorised along several dimensions.wikipedia
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grammar schoolsGrammarGrammar schools in the United Kingdom
juniorjunior schoolsprimary school
lower schoolfirstfirst schools
junior high schoolmiddlejunior high
Many jurisdictions have no formal "middle" level between primary school and secondary school, but in those that do, "middle school" is a generic term for it.
preparatory schoolprep schoolpreparatory
In England, a "preparatory school" is a specific type of middle school.
high schoolsecondaryhigh schools
vocational-technicalvo-techtechnical high schools
comprehensiveComprehensive Public High SchoolHigh School
secondary modernhigh schoolsecondary modern schools
sixth-form collegesixth formsixth form colleges
college preparatorypreparatory schoolcollege preparatory school
A special note about the term "college": in North American and especially US usage, this is a truly generic term for all post-secondary education, right up to and including university, but can also be understood to mean a smaller, four-year, baccalaureate institution.
liberal artsliberal arts universityliberal arts colleges