Major spoilers for "Beyond the Wall" (Game of Thrones, S07E06)
In "Beyond the Wall" (Game of Thrones, S07E06) we see the newest member of the army of the dead ...
Viserion, one of Daenerys' three dragons, was killed and we see the Night King himself resurrect the beast, and we see it wake up with blue eyes.
Usually, from what we have seen (particularly in "Hardhome" (Game of Thrones, S05E08)), a dead thing can be resurrected as a wight from a distance, remotely, and any White Walker can cause the turn.
But a White Walker is exclusively created by the Night King touching the victim (again, from what we've seen), other than the way the original White Walker was created.
Just looking at these two different methods of resurrection, the way Viserion is resurrected seems much more similar to the White Walker type than the way wights are made. It's possible that turning dragons is an entirely different puzzle, even to a wight, so the Night King had to see this through, personally, and touch him.
The difference between a barely conscious, telepathically controlled drone of a wight and a seemingly more conscious, self-aware and powerful White Walker is significant enough that it warrants having an answer.
Is Viserion a wight or a White Walker?