1. This is the same watch that I lost.

2. This is the watch that I lost.
3. This is the very watch that I lost.
4. This is the same watch as I lost.
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Do #1, 2, and 3 have the same meaning?
They mean that I found that I had lost, right? #4 means that this is the same kind of product that I lost, but it is not the watch I lost. Is this right?

1, 2, and 3 are fine.

4 wouldn't be used.

#1, #2, and #3 have similar meanings but with subtle differences. They all convey that the watch being referred to is the one that the speaker lost. However, #1 and #3 add emphasis to the statement.

#1 "This is the same watch that I lost." emphasizes that the watch being referred to is identical to the one the speaker lost.

#2 "This is the watch that I lost." simply states that this watch is the one the speaker lost, without emphasizing sameness.

#3 "This is the very watch that I lost." adds extra emphasis to convey that this watch is precisely the exact same one the speaker lost.

As for #4, "This is the same watch as I lost," it actually has a different meaning. It suggests that the speaker found a watch that is exactly the same as the one they lost, but it is not the actual watch they lost. So, your understanding is correct. #4 conveys that it is a watch of the same kind as the one the speaker lost, but not the specific watch they lost.