The instance of the inner class is created when instance of the outer class is created. Therefore the members and methods of the inner class have access to the members and methods of the instance (object) of the outer class. When the instance of the outer class goes out of scope, also the inner class instances cease to exist.
The static nested class doesn't have a concrete instance. It's just loaded when it's used for the first time (just like the static methods). It's a completely independent entity, whose methods and variables doesn't have any access to the instances of the outer class.
The static nested classes are not coupled with the outer object, they are faster, and they don't take heap/stack memory, because its not necessary to create instance of such class. Therefore the rule of thumb is to try to define static nested class, with as limited scope as possible (private >= class >= protected >= public), and then convert it to inner class (by removing "static" identifier) and loosen the scope, if it's really necessary.