Terminology quibble:

I get where you get this notion of connotation from, but there's a more formal one that Quine used, which is at least related. It's the difference between an extension and a meaning. So the extensions of "vertebrate" and "things with tails" could have been identical, but that would not mean that the two predicates have the same meanings. To check if the extensions of two terms are identical, you check the world; it seems like to check whether two meanings are identical, you have to check your own mind.

Edit: Whoops, somebody already mentioned this.