Perhaps the name is just translating oddly. He lets the matter drop-- he's really not in a place to care right now, nor to focus on anything but Thingol, the other's presence a constant beacon, a yearning to stop whatever he's doing and bask in his lord being here. Again. After so long.

"Quendi. Elves," Thranduil agrees, and draws his hand back to his side. "It would depend on the elf you asked, who was being greeted, when, and why. Just as it is for Men."

He can't speak on Dalish greetings, but doesn't bother making the distinction in the differences between the kind of elf he is, and the kind Beleth is.