school for children aged 12 to 18 in the UK
secondary school
higher education, where people study for an undergraduate (= first) or postgraduate (= higher level) degree
university (UK), college (USA)
a school for children between the ages of about 5 and 11 in the UK
primary school
a school for children from about 9 to 13 years old, usually grades 6-8, "junior high school"
middle school
basic schooling in the USA, usually grades 1 through 5
elementary school
time frame during the semester, usually a few months long
terms
a school for young children, particularly those between the ages of 3-5 (in the USA, pre-school)
nursery school
a school which provides accommodation and meals for the pupils during term time.
boarding school
in the UK, a school that is free to go to because the government provides the money for it (in the US = a college that is funded by the state)
state school
teaching, schooling, tutoring
education
a class or school that prepares children, usually 5-6 year-olds, for the first year of formal education
kindergarten
school at home
homeschooling
a school for teenagers usually including grades 9-12
high school