In the UK it’s primary = age 5 to 11, secondary = 11 to 18, tertiary = 18+, e.g. university or college.

Primary school is where you learn all your basics.
Counting, reading, writing, math skills etc.
This is for kindergarten – 8th grade (at least in North America)
Classes are small – up to 30 students – and you have one teacher everyday, all day for the year

Secondary school is where you expand on the basics and study subjects that you want to use in your career.
Classes can get really detailed and focus only one one thing.
This is for grades 9 – 12 (some 13)
Classes are still small, but are only for 75 minutes a day and you rotate between teachers, classrooms and students.

Tertiary school is the most important, you are getting certification for what you will spend the rest of your life doing.
Classes can be from 10-500 + students with one Professor.
Teachers/Professors will not hold your hand and you are going to be very independant.
You may have entire days without classes, one class a day etc.
These schools are also very expensive and students may live at the school.