primary and secondary

With slight variations in some geographical areas, yes, that's right. (I'm assuming that by "your country" you mean the USA.

After secondary education, it's called post secondary. That's becaues too many people are unsure of the pronunciation of tertiary.

...or even the meaning of the word in many cases.

I'm assuming that by "your country" you mean the USA.

[rolls eyes]

In Canada, we use elementary school to refer to Kindergarten through the end of Grade 8. Grades 9 through 12 are found in secondary school here, as is the OAC year in Ontario.