it seems there are many high schools in England.
The high school I went to in the NE of England was called King Edward VI High School (tens of thousands of pupils, possibly over 100,000 have gone through it) by everyone. It is years 9, 10, 11, 12 and 13. Before that I went to a first school (up to year 4), then a middle school (years 5-8).
The town we lived in once we were married had 2 high schools. Both years 9-13. One side of the town went 2-tier and became an academy. Now it's years 7-13 and referred to as X name, but officially is X name campus, but nobody says that. They are now really primary schools and a secondary, but that was just changing as we left the area.
In the SW of England, where we are now, I have had to adjust to saying primary and secondary school as they are all referred to as that. Primary being years reception to 6 and secondary being years 7 to 11 or 13, depending on if they have a sixth form.
I have always assumed a high school is years 9 - 11 (or 13), so the three tier system and a secondary school is years 7 - 11 (or 13), so a two tier system, but I might be wrong if others refer to secondarys as high school. I thought high and secondary were slightly different with how many years they cater for.