According to the GFSZ a school is where accredited instruction in any of the grades K - 12 takes place. Schools do not stop being schools on the weekends or during school vacations, or when the local community players put on "The Sound of South Pacific''s Seven Brothers*".
Public schools, parochial schools, independent/unaffiliated schools. If it has just a nursery school/day care center it is not a school. Some of the church schools are pre-K to grade 3 or 4. They are GFSZs. Because the school part has an inside physical connection to the rest of the building, the whole place is a GFSZ. (And I'm not eager to go to federal court and put up a defense that because the church building is not physically connected to the school I should be allowed a pass for bringinng a gun to church (otherwise legal where I live).
And remember, the GFSZ extends 1000 feet from the outer boundary of the school property, not from the outside of the school building.
* - It was a great musical comedy. Have not laughed so much since seeing that several years ago.