Full Idea
The 'mental representations' of Earth speakers and Twin Earth speakers were not in any way different; the reference was different because the substances were different. Reference is fixed by the environment itself.
Gist of Idea
Reference may be different while mental representation is the same
Source
Hilary Putnam (Representation and Reality [1988], §2 p.32)
Book Reference
Putnam,Hilary: 'Representation and Reality' [MIT 1992], p.32
A Reaction
There seems to be an elementary distinction here between what you think you are referring to, and what you are in fact referring to. "That man is the Prince of Wales" (pointing at the butler).