Does your state use the term "unified school district"?

no. and not clue what unified means. I know some schools in our state does use the term, but it seems to be in the big cities.

Yes, schools in most countries are organized by state, city, district then elementary, middle and high school. They are supposed to have a supervisor for a certain amount of schools and this is how they keep record, so in Mexico they include public and private schools, as they need to be supervised also.

Many towns organized into larger school districts especially for high school. There might be a town which as its own elementary district and the same town might have a unified high school district. In larger cities that tend to merge together, years ago the smaller districts merged into one large or unified one. It could be called something else in another state.

It's just several small schools combined up to form a pact for certain areas. I think Japan has this, not sure what other countries have it.