A secondary school describes an institution that provides secondary education and also usually includes the building where this takes place. Some secondary schools provide both lower secondary education (12 to 15 years of age) and upper secondary education (15 to 18 years of age) ie levels 2 and 3 of the ISCED scale, but these can also be provided in separate schools, as in the American middle and high school system. In the UK, elite public schools typically admit pupils between 13 and 18 years of age. UK state schools accommodate pupils between 11 and 18 years of age.
In the ISCED 2011 education scale levels 2 and 3 correspond to secondary education which are as follows:
Lower secondary education- First stage of secondary education building on primary education, typically with a more subject-oriented curriculum. Students are generally around 12-15 years old
Upper secondary education- Second stage of secondary education and final stage of formal education for students typically aged 16–18, preparing for tertiary/adult education or providing skills relevant to employment. Usually with an increased range of subject options and streams.
Terminology: descriptions of cohorts
Within the English speaking world, there are three widely used systems to describe the age of the child. The first is the 'equivalent ages', then countries that base their education systems on the 'English model' use one of two methods to identify the year group, while countries that base their systems on the 'American K-12 model' refer to their year groups as 'grades'. The Irish model is structured similarly to the English model, but have significant differences in terms of labels. This terminology extends into research literature. Below is a convenient comparison 
Secondary cohorts- description used in US, UK and ROI
School building design does not happen in isolation. The building (or school campus) needs to accommodate:
Education within the political framework
Use of school building (also in the community setting)
Constraints imposed by the site
Each country will have a different education system and priorities.  Schools need to accommodate students, staff, storage, mechanical and electrical systems, support staff, ancillary staff and administration. The number of rooms required can be determined from the predicted roll of the school and the area needed.
According to standards used in the United Kingdom, a general classroom for 30 students needs to be 55 m2, or more generously 62 m2. A general art room for 30 students needs to be 83 m2, but 104 m2 for 3D textile work. A drama studio or a specialist science laboratory for 30 needs to be 90 m2. Examples are given on how this can be configured for a 1,200 place secondary (practical specialism). and 1,850 place secondary school.
Building design specifications
The first taxpayer-funded public school in the United States was in Dedham.
The building providing the education has to fulfil the needs of: The students, the teachers, the non-teaching support staff, the administrators and the community. It has to meet general government building guidelines, health requirements, minimal functional requirements for classrooms, toilets and showers, electricity and services, preparation and storage of textbooks and basic teaching aids.  An optimum secondary school will meet the minimum conditions and will have:
adequately sized classrooms;
specialised teaching spaces;
a staff preparation room;
an administration block;
a general purpose school hall;
laboratories for science, technology, mathematics and life sciences, as may be required;
a library or library stocks that are regularly renewed; and
Government accountants having read the advice then publish minimum guidelines on schools. These enable environmental modelling and establishing building costs. Future design plans are audited to ensure that these standards are met but not exceeded. Government ministries continue to press for the 'minimum' space and cost standards to be reduced.
The UK government published this downwardly revised space formula in 2014. It said the floor area should be 1050m2 (+ 350m2 if there is a sixth form) + 6.3m2/pupil place for 11- to 16-year-olds + 7m2/pupil place for post-16s. The external finishes were to be downgraded to meet a build cost of £1113/m2. 
A secondary school locally may be called high school or senior high school. In some countries there are two phases to secondary education (ISCED 2) and (ISCED 3), here the junior high school, intermediate school, lower secondary school, or middle school occurs between the primary school (ISCED 1) and high school.
Names for secondary schools by country
Argentina: secundaria or polimodal, escuela secundaria
Iceland: framhaldsskóli (menntaskóli, iðnskóli, fjölbrautaskóli) from 11-13 Grade. You go first in 1 - 10 Grade then you change the school to Menntaskóla and take 3 years (11-13 Grade). But you can also take it 4 years.
Indonesia: sekolah menengah atas (SMA) (lit. "upper middle school"), sekolah menengah pertama (SMP) (lit. "first middle school"), sekolah menengah kejuruan (SMK) (vocational school, lit. "middle vocational school")
Israel: Bet Sefer Tichon (בית ספר תיכון) (literally middle school, but in reality grades 9-12)
Italy: scuola secondaria di primo grado (3 years) + scuola secondaria di secondo grado (5 years): Liceo, Istituto Tecnico and Istituto professionale
Japan: chūgakkō (中学校; literally middle school), kōtōgakkō (高等学校; literally high school), chūtōkyōikugakkō (中等教育学校; Secondary School) – In the pre-Meiji educational system, the equivalent was called "chūsei"
South Korea: 중고등학교(中高等學校・Chung'godŭnghakkyo), 중등교육 (Chungdŭng'gyoyuk; literally middle education), comprising 중학교 (Chunghakkyo; the Lower secondary school, years 7–9, though referred to as "middle school grades 1–3") and 고등학교 (Kodŭnghakkyo; the Upper secondary school, years 10–12, though referred to as "high school grades 1–3")
Spain: educación secundaria, composed of two cycles: E.S.O. (Educación Secundaria Obligatoria, compulsory secondary education, 4 years, 7th to 10th grade) and bachillerato (non-compulsory secondary education, 2 years, 11th and 12th grade); formerly (for those born until 31 December 1983), primary education comprised up to the 8th grade and the secondary education was composed of two non-compulsory cycles: B.U.P. (Bachillerato Unificado Polivalente, 3 years, 9th to 11th grade) and C.O.U. (Curso de Orientación Universitaria, 1 year, 12th grade)
Sri Lanka: junior secondary school, senior secondary school
United States: High school (North America) (usually grades 9–12 but sometimes 10–12, it is also called senior high school) is always considered secondary education; junior high school or intermediate school or middle school (6–8, 7–8, 6–9, 7–9, or other variations) are sometimes considered secondary education.
Uruguay: Liceo or Secundaria (3 years of compulsory education: Ciclo Básico; and 3 years of specialization: Bachillerato Diversificado, into: Humanities (Law or Economics), Biology (Medicine or Agronomy), Science (Engineering or Architecture), and Art
Vietnam: Trung học cơ sở (abbreviated THCS, lit. "basic middle school", equivalent to junior high school in the U.S.); trung học phổ thông (abbr. THPT, lit. "general middle school", equivalent to senior high school in the U.S.)
^"International Standard Classification of EducationI S C E D 1997". www.unesco.org. Archived from the original on 2017-03-19. Retrieved 2017-03-12.
^Iwamoto, Wataru (2005). "Towards a Convergence of Knowledge Acquisition and Skills Development" (PDF). uis.unesco.org. UNESCO. Archived from the original (PDF) on 2017-05-25. Retrieved 11 March 2017.
^ abWard, Ken. "British and American Systems (Grades)". trans4mind.com. Retrieved 30 March 2017.
^Liew Kok-Pun, Michael (1981). "Design of secondary schools:Singapore a case study" (PDF). Educational Building reports. Voume 17: UNESCO. p. 37. Archived from the original (PDF) on 2017-04-04. Retrieved 3 April 2017.CS1 maint: location (link)
^"Baseline designs: 1,200 place secondary (practical specialism) - GOV.UK". www.gov.uk. GOV.UK. Retrieved 4 April 2017.
^"Baseline design: 1,850 place secondary school - GOV.UK". www.gov.uk. gov.uk. Retrieved 4 April 2017.
^ ab"Guidelines relating to planning for public school infrastructure". Department of Basic Education, Republic of South Africa. 2012. Retrieved 3 April 2017.
^"Baseline designs for schools: guidance - GOV.UK". www.gov.uk. Education Funding Agency. 11 March 2014. Retrieved 3 April 2017.
Wikimedia Commons has media related to High schools and secondary schools.
Australian CensusAtSchool (Australia)
Canadian Education Statistics Council (CESC) (United States)
Office for National Statistics (ONS) (United Kingdom)
BB103_Area_Guidelines_for_Mainstream_Schools (2014) UK
National Center for Education Statistics (NCES) (United States)