Another idiosyncrasy. "Elementary school" goes kindergarten, first grade, second grade, ..., fifth grade; then "middle school" is sixth, seventh, and eighth grades; but high school is freshman, sophomore, junior, and senior, and it's very common to just say ninth grade, tenth grade, eleventh grade, and twelfth grade interchangeably with the former terms. Finally, you can say "grade one" and "first grade," "grade two" and "second grade," etc., interchangeably as well.
First grade being the second classroom for most kids is how they get an intuitive sense for cardinal, nominal, ordinal, interval and ratio.[0] Some learn it later in life where a second class private outranks a private but not a private first class.[1]
An extra twist in the US is elementary school tends to end at 6th grade and middle school is 7th and 8th or sometimes elementary ends a year early at 5th and middle school absorbs 6th grade to be 3 years long.
It's not so much that there's a formal standard for what years "should" be middle school in the US.
School districts in the US almost always start without established middle schools. Instead, there's so much elementary school capacity and so much secondary school capacity in a district. And then, whenever the population of students in the district changes, the choices of the district school board to respond to that are either to:
1. build one additional elementary school for every N additional grade 1-7 students, and/or one additional secondary school for every M additional grade 8-12 students (and continue to pay these CapEx costs even if student population goes down; and agree to deal with the fact that growth in elementary students will inevitably propagate to growth in secondary students 7 years later);
2. add temporary capacity to existing elementary + secondary schools with portable classrooms (which can easily be reduced back down if populations decrease — but which don't come with commensurate increases in central infrastructure, eventually straining the capacity of school facilities);
3. or, at one point, you look at the numbers of students in each year in your district, treat the years as vnodes, and then rebalance a contiguous set of those vnodes to a new "shard" called "middle schools". I.e. you pick a set of school-years, where extracting students from that set of years from one or two elementary and secondary schools in the district into a newly-built middle school, will result in a "good" amount of capacity being freed from those schools, and the resulting middle school instantly having a "good" utilization.
Once you've chosen option 3 one time, it sets a precedent in that district for what years middle school should cover in that district. Most districts only do the study for what years would be best to extract out the first time they build a middle school. After that, they just go with what they did before, even if it's no longer optimal (because skipping the study saves time and money.)
In theory, school districts could actually build successive middle schools that "pull" different years of utilization out of the elementary+secondary schools around them than previously-built middle schools have. The only issue would be in administrative assignment of students to schools — this would require you to place middle schools with different year coverage so they never have overlapping catchment area.
