When recently LEAVING Thailand via Bangkok (BKK) airport I used the priority lane for business and first class passengers near check-in desks section S/T/U.

At this particular departure point the word "fast track" was present on various permanent fixed physical signs (not just electronic displays) both when entering the reserved departure area, and also when waiting to see the immigration officer. This fast track section included both the security checks, and also passport checks. It worked very quickly and I went through both security and passport check, in less than 15 to 20 minutes for everything.

I'm not sure if it's the same elsewhere in the airport as there are obviously many other check in desks starting from the letter A all the way to R, and then onto the sections S/T/U (where I was) so there may (or may not) be variations at the other fast track/priority departure sections.