Other than not hating it 
This was my school system.
Hey! We overlap in time and location. Robert Frost Intermediate for 7-8 and Thomas S. Wootton for 9-12.
In Baltimore County in 1963-75 it was
Elem K-6
Jr. High 7-9
Sr. High 10-12
My high school (Loch Raven) was an exception for one year. I was a sophomore the first year it was opened. They didn’t want to pull seniors out of their schools for one year so they filled the space with 9th graders.
Today in Fairfax County, Va., it’s
Elem K-6
Middle 8-9
High 10-12
I went to Catholic school, 1st through 8th grades, then on to High School (9-12).
You get 7th grade off? Sweet.
I moved and changed schools between 10th and 11th grade.
First school, Jr High 7-9, Sr High 10-12. The year after I left, the HS changed to 9-12. Don’t know whether the Jr High went to 7-8 or 6-8.
2nd school was 10-12, split sessions 11&12 in am, 10 in pm. New HS nearby was under construction. After the new HS was built, probably went regular days, no split.
Doesn’t seem to be any set way. I’ve seen jr highs that were just 7 & 8, I’ve seen some that also included 9. I’ve seen some that changed their name to middle school despite still being 7 & 8, others still jr high. Middle school seems to be the prevalent term these days, but jr high is definitely still around here and there.
Where I am 6th grade was always elementary, but in another part of the state I know of a place where elementary was k-4 and middle school was 5-8.
Intermediate, only place I’ve seen that used is an entirely different thing, some sort of resource center for teachers. Also they run the “short buses” for all the local schools.
One school district in the town I grew up in had a large elementary and a high school., with high school being grades 9 and up. Grades 6 - 8 were in a different wing than the younger kids. There were other schools in smaller communities that also fed into the high school.
The other district had multiple elementary schools feeding into a Jr. High/Middle School, which was grades 7 and 8.
We had a rather weird system where it was:
1-7 Elementary
8-12 High School
6th and 7th graders, though, were set up to change classes for half the day-- special teachers for math, PE and science. All the same kids, but we changed class rooms. Our “main” teacher taught us all English, History, Social Studies.
8th graders were called pre-Freshmen. We were the lowest of the lows, but we didn’t care. We were in efin’ High School, baby!!
Middle 5-8
High school 9-12
Upstate NY. There was no separate Jr. High.
The middle school used to be 4-8, before I attended, which was in the 90s. A few years later, they moved the 5th graders down to the elementary school.
In my school district (also SF Bay Area), the junior high school was 7-8; when it was changed to 6-8, the name was changed to middle school. (It’s now 5-8, and still called middle school.)
I always considered “intermediate school” to be something like 4-8, mainly because at my elementary school, 1-3 were “primary” grades and 4-6 were “intermediate”. The only real difference was, primary grades were one hour shorter because the first and last hours were reserved for teaching reading, one of which was for the weaker readers and the other for the better ones (mainly to be able to concentrate on the weaker ones without holding the better ones back as a result).
Around these parts they’re lower (k-3) and upper (4-6) elementary (or el, as they say in shorthand). Same building, just how you refer to the younger kids vs the older. Depending on the building size and layout might be in different wings.
Back in my day, Fairfax County had Elementary (K - 6), Intermediate (7-8), and High School (9-12). There were also a few secondary schools which had 7th and up (no idea if the 7-8th graders had an entirely separate part of the building or not).
Before they adopted the intermediate school concept in 1960, elementary schools went through 7th grade and high school started at 8th.
Over in DC, Junior High went 7th-9th and high school didn’t start till 10th grade.
Primary school: K-3 (sometimes informally called “little school,” never “elementary school”)
Middle school: 4-6
Junior high: 7-8
High school: 9-12
I went to public school in Fairfax County from 1998-2007 and it was elementary school K-6, middle school 7-8 and high school 9-12.
Prior to living in VA and going to public school I went to a Montessori school in Illinois that was divided into preschool and kindergarten, “lower elementary” (1-3) and “upper elementary” (4-8) at which point kids had to find a different place to go for high school. I’m not sure if Montessori high schools exist.
I went to a junior high school as defined in OP.
Our middle school was 6-8. And as for these philosophies, what you call the middle school one is how 6th grade worked, while 7-8th were exactly like our high school.
Michigan, early and mid 1960s. Grade school was K-6, junior high was 7-8, high school was 9-12. Beginning the year I was in sixth grade, though, it was K-5 for grade school and 6-8 for junior high.
Illinois, late '60s. The same K-6 grade school, 7-8 junior high and 9-12 high school that we’d started with in Michigan.
CT, now. K-5 grade school, 6-8 middle school and 9-12 high school. (When I was stationed here in the early '80s it was the same as what I knew from Illinois, but they changed to the current system sometime in the late '80s.)