Hmm, I don't really understand what you're asking but here's what I know:

== compares references
Equals() compares String literals

If you want to be able to use == for equality checking, look into the String.intern() method. It (a) incurs an immediate speed penalty and (b) makes equality checking (with other strings that are known to be interned or final) into a pointer comparison.

Check out the API. As usual, it's pretty detailed on it. Basically, you should never use == to compare strings, sometimes to equal strings will return true even though you didn't make them reference to the same string object. Using String.equals() is usually best.

== will always compare object identity (reference comparison), as it does for any Object in Java.
.equals() and .compareTo() will always compare object value (value comparison; i.e. string comparison for Strings), assuming they are written appropriately (and you can rest assured they are for java.lang.String ;) ).

However, since String objects are immutable, it becomes possible to "intern" strings. A string which has been intern'd (short for internalized, I'd guess) behaves like any statically-known-at-compile-time String; which is to say, there will be only one String in memory with that given value. Subsequent attempts to make a new String with the same value will instead reference the old String, which is OK because it's immutable. (I'm not sure if this will fix references to existing Strings with the same value, or how that works, if so.)

Here is an interesting topic in a blog from someone working at sun:
http://blogs.sun.com/roller/comments/dreamwords/Weblog/can_i_use_to_compare