instanceof

i understand the very basic gist of 'instanceof'. however, there are details i don't understand. to dive straight to my situation, consider the following code:

try {
  asYouMight();
} catch (Exception e) {
  if (e instanceof ArrayOutOfBoundsException) {
    doSomethingVeryDifferent();
  } else {
    throw new fit(e);
  }
}

so, it appears to my relatively novice eyes that instanceof can test an instance of an object for ANY subtype, right?

i kinda don't get it, and i want to. does 'e' still have all of the "ArrayOutOfBoundException-specific" fields and methods, or does it lose them because it was "caught" as an "Exception"? i know AOOBE doesn't have much in the way of separate fields and methods from a normal Exception, but other classes may -- perhaps this code better illustrates:

public void aMethod( SuperClass a ) {

  if (a instanceof SuperClass) {
    a.methodOnSuperClass();
  } else if (a instanceof SubClass) {
    a.methodOnSubClass();
  }
}

would that work?