Did you attend elementary school or grammar school? Or did you go to a grade school or primary school? Or perhaps a public school or a magnet school?
I find it interesting that we have so many terms for what is essentially the same thing, the school we attend before high school, which except for the more formal secondary school has been called the same thing for generations. Schools that house the lower grades, however, have been called a variety of names depending on when and where those schools were located.
Back in northwestern Ohio in the 1950s, I attended grade school. My son, 100 miles away in the 1980s, went to a private elementary school. My parents may have attended a grammar school in the 1920s, also in northwestern Ohio. I'm not really sure what they called it.
Grammar school, at one time, had more to do with Latin grammar than English grammar. And sometimes it was more likely to be a secondary school than a primary school. Such schools were originally intended for the more elite students, those taking classic courses, such as Latin. In time the name became more generally applied to primary schools. A magnet school today seems to have something in common with the original idea of a grammar school.
Public school, to most of us in the United States, simply means a school, elementary or secondary, that is supported by taxpayers. In New York City, however, the term is more narrowly applied to elementary schools, such as P.S. 3. In England, a public school is not supported by the government, in that same way that a public house, or pub, is privately owned.
Today elementary school seems to be the most widely used term, even though it is a bit long and cumbersome when either writing it or saying it. I much prefer grade school.