The Mirrorball Man
Aventurier
Well the thing about "distinct vibe" is that it can only really be described by itself, so the Realms' distinct vibe is "Realmsian" - it is just the feeling of the Forgotten Realms, from Waterdeep and Khelben Arunsun to Anauroch to the Dalelands and the Zhentarim, to the Harpers and Selune's Tears. The distinctness isn't obvious like, for instance, Tekumel or Talislanta. It is relatively subtle, or at least more so than more obviously unique or exotic settings. But distinctness need not be obvious, just as originality need not be blatantly novel.
Thank you for your answer, but that doesn't make a lot of sense to me. If there's something distinct about the Realms, even if it's subtle, one should surely be able to express it in some way. And if it's one of these things where one has to experience it in order to understand it, well, I've experienced it, and didn't find anything distinctive about it.