What to call Primary School + High School, but not College
Solution 1:
The answers and comments to this question have already demonstrated that it varies across the country. I would have answered that the terms "Primary School" and "Grade School" both refer to elementary, middle, and high school collectively.
According to Wikipedia, the government considers "elementary school" to cover anything up to grade 8, whereas in my experience it's only considered to extend to grade 5.
Because of these ambiguities, I think that "K-12" is the only real answer to your question that works regardless of who the user is (as long as they're from the US.)
Solution 2:
If you used the categories Pre-College and College, I think people could easily determine that "pre-college" refers to grades 1-12.