why variable defined in a class is not a local variable but instance variable in java?

According to the doc Local variables in java are declared in methods, constructors, or blocks.

In the below Class A isn't x a local variable too since it is in blocks({}) i know they are called as instance variable but i am confused? If yes Access modifiers cannot be used for local variables but i am sure i can add public private protected ? It also says that local variable are stored in stack but as per the below code x will be stored in heap right since they are part of the instance?

class A{

private int x = 5; // Isn't this a local varibale too since it is in blocks 

}

.

class A{

public void function(){
int x = 5; // this is a local variable since it is declared in a function
private int x2=5; // Error Access modifiers cannot be used for local variables
}

}