1. This is the same watch that she gave me.

2. This is the same watch as she gave me.
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What is the difference between them?
Does #1 mean: "This is the very watch that she gave me."?
Does #2 mean: "This is the same kind of watch, which she gave me. It's not the very watch that she gave me."?

Those two sentences seem to be intended to mean the same thing, but the second one is the smoother sentence.