What is the difference between public schools and international schools?

Well, the two main differences are...

Public: For the locals/natives.

International: For visitors/foreigners.

Public: Free.

International: Usually have to pay.

Academics in international schools shall have roughly the same requirements as the international student's home school since international schools only associate and adapts to certain schools in other countries. The thing about international school, also, is that most typically have dorms/boarding rooms (usually from middle school - college) for their students whereas public schools don't. They can also provide families who volunteer to take care of a student and will share their home with them. Or, a third case could be that a student's whole family decided to pack up into another country and are staying at an apartment (usually for work purposes or something) and the student cannot speak the language of that country, so international schools will often consists of teachers who speak all sorts of languages to teach in the language that a handful of their students are most familiar with.