The fact that the original game was a mod is an implementation detail; it's basically irrelevant for us. A question tagged the-stanley-parable-mod sounds like a question about a mod for The Stanley Parable.
Using the year of release date is both unambiguous, clearer and it's consistent with what we've been doing.
As one who has played all 3 versions, I (Batophobia) can verify that each one is different.
I suggest changing the questions about the mod to the-stanley-parable-mod and leaving the questions about the full game as the-stanley-parable. As for the demo, it can probably remain under the full game tag and maybe add the demo tag to it.
(This self-answer moved from the question to this CW for voting purposes.)