Primary School = Elementary
Lower Secondary = Middle School
Upper Secondary = High School
Well almost, Lower/Upper Secondary can be different. In most Commonwealth countries, they treat Lower Secondary (Grade 7, 8, 9) and Upper Secondary (Grade 10 and 11). (Edited)
They also have "Sixth Form College" (Grade 12). It is not technically college, more like a Pre-university. They call it "Junior College" here in Singapore.
I studied in an American school for a few years then changed to GCE Curriculum (in an international school) to finish my Secondary academics. Took both SATs and O Levels though. However, I opt out for A Levels.
I think it's years 7 8 and 9 that are lower secondary
as evidenced by the fact I used to wear red in those years and blue in years 10 and 11
Idk maybe i'm wrong or my school was wrong