The terminology isn't necessarily standardised even across the UK, and things change with time. When I was a child, I went to "first school" (age 5-8) then "middle school" (age 8-12), and then secondary school (12-16).
My first school and middle school are still in existence and are now called "primary school" and "junior school". The junior school, as I understand it, is now for children aged 8 to 11. These days, kids move up to secondary school at 11, a year younger than when I was a child.