public school, state school

academy (specialized school), vocational school

private school (US), public school (UK)

military academy, (especially) the Imperial Japanese Naval Academy

(historical) elementary school, national elementary school

school supported by a pro-South Korean organization

school supported by a pro-North Korean organization

school grammar / (specifically) Japanese school grammar, based on Shinkichi Hashimoto's work and now universally employed in Japanese schools and dictionaries.

school for special needs

driving school