All states have historically made a distinction between two genres of K-12 education and three genres of K-12 school. The genres of education are primary and secondary; and the genres of school are elementary school, middle or junior high school, and high school (historically, "senior" high school to distinguish it from the junior school).
Primary education (or "primary school" meaning "primary education") still tends to focus on basic academic learning and socialization skills, introducing children to the broad range of knowledge, skill and behavioral adjustment they need to succeed in life - and, particularly, in secondary school. Secondary education or secondary school has always focused on preparing adolescents for higher education or/and for careers in industries, trades or professions that do not require an academic degree.
The elementary school has always been the main point of delivery for primary education; and the (senior) high school has always been the focal point of secondary education. Originally, elementary school was synonymous with primary education, taking children from Kindergarten through grade 8; and secondary school was entirely coextensive with the high school grades 9 - 12. This system was the norm in America until the years following World War I, because most children in most parts of what was then the mostly rural United States could go no further than Grade 8. Even when the high schools were available, they were often not accessible.