What is the difference between 'open' and 'public' in Kotlin?

The open keyword means “open for extension“ - i.e. it's possible to create subclasses of an open class:

The open annotation on a class is the opposite of Java's final: it allows others to inherit from this class. By default, all classes in Kotlin are final, which corresponds to Effective Java, Item 17: Design and document for inheritance or else prohibit it.

You also need to be explicit about methods you want to make overridable, also marked with open:

open class Base {
    open fun v() {}
    fun nv() {}
}

The public keyword acts as a visibility modifier that can be applied on classes, functions, member functions, etc. If a top-level class or function is public, it means it can be used from other files, including from other modules. Note that public is the default if nothing else is specified explicitly:

If you do not specify any visibility modifier, public is used by default, which means that your declarations will be visible everywhere

class A { ... } in Java is equal to open class A { ... } in Kotlin.
final class B { ... } in Java is equal to class B { ...} in Kotlin.

It is not related with public.

In Kotlin, everything without access modifiers is public by default. You can explicitly say public in the definition, but it is not necessary in Kotlin.

So,

public class A { ... }

and

class A { ... }

are the same in Kotlin.