The "state" you talk about is not the state of the class, but the state of the instance. Don't think of a class as a physical thing. A class is just a description of what an instance of that class has (properties) and does (methods). Think of what a person is. You know in your mind what makes a person, what a person can do, etc, but that knowledge in your mind cannot walk and talk. It's just an abstract concept that describes a person. It's not an actual person. That's what a class is. It's just an abstract description. Each person you know is an instantiation of that idea in your head. Each person you know is an instance of the Person class.
I'm not 100% sure what you're last question means but I'll assume that you're asking about the difference between reference equality and value equality. If so then, sticking with the person analogy, consider identical twins. They are an example of value equality. Everything about them is the same, so they are equal in that sense, but they are still two distinct people. On the other hand, if I refer to my mother and my father's wife then I am making two different references to the same person.