British:
I don't get the difference between public and private schools? Sounds to me like it's the same. For example what kind of school is Eton? Eton College is a Public School, and at the same time a private [independent] school being funded by the fees charged for attendance and charitable funding and not supported by the state. Private schools are owned by someone, charge fees for attendance, and are not supported by the state - see here for lots of information: http://www.privateschools.co.uk/index.htm
I don't understand grammar schools. What does "selective" mean? If the pupils have to do good academically to get in, it sounds like a private school but then it's state funded ... This is historical and the best thing is to refer you to this for more information:http://en.wikipedia.org/wiki/Grammar_school
What are A levels and GCSE? (no long explanation needed, I just need to get the basic idea) A levels = Advanced level General Certificate of Education - there were three levels: Ordinary Level, Advanced Level, and Scholarship Level. GCSE = General Certificate of Secondary Education.
What is undergraduate? Post graduate? An undergradute is a student studying for a first degree. Once that first degree has been achieved, and he or she goes on to do research for a second degree, they are post[after]-graduates.
Is this correct?
State School
USA: Funded by the state. (usually Uni)
UK: Funded by the state
Private School
USA/Canada: supported by the state
UK: Funded by parents. Also called independent schools, has a rep of high academic standars.
Public School
USA/Canada: supported by the state
Scotland: supported by the local authority
UK: Funded by parents. Private or independent, often single sex. Expensive and prestigeous. Refers to several private schools. Now usually also has charitable status. {sorry to add another confusion!}
Elementary School (am) / Primary School (br)
USA/Canada: Regular school, 5-13 years old.
UK: Regular school, 5-11 years old.
Secondary School
USA/Canada: 14-18 years old. Grade 9-12 (at times 10-12) aka High School.
UK: 11-16 or 11-18 years old. Grade ????-????
Grammar School
USA/Canada: same as elementary
UK: State funded. Selective secondary school, students have to academically compete to get in.
College
USA/Canada: college and uni are the same. College=undergraduate degrees. Uni=post graduate degrees
UK: 16-18 years old. A-levels. It is more complex than that - did you look at the site I posted?
University
UK: degree and post graduate studies.