First of all, there's no Night King in the books. The showrunners made him up to give the characters a nice big clearly designated target. The White Walkers (known in the books as "Others," but Lost kinda stole that name) are far from mindless, silent monsters whose only motivation is "kill all humans." Not only do they have speech (like "the cracking of ice on a winter lake"), but it's also recognizable enough for humans to infer tone. We know this because in one scene, they're speaking to "mock" one of the brothers of the Night's Watch, presumably on account of his pathetically tiny sword.
To aid in the making of the graphic novel adaptation, George R.R. Martin described the Others as "strange, beautiful ... think, oh ... [fairies] made of ice, something like that ... inhuman, elegant, dangerous." Only the "made of ice" part seems to apply to Game Of Throne's ugly-ass White Walkers. This makes sense, because Martin has also said that he doesn't "want to write about the band of heroes on one side and the orcs on the other," and that he dislikes fantasy stories where the races are defined by a single personality (orcs are evil, elves are snobbish, hobbits are sex fiends, etc.).
When an audience member asked specifically about the Others, Martin declined to comment. Normally we'd assume he was trying not to crap all over the show that made him rich, but this was before the show even started, so we're assuming he didn't want to spoil some plot twist regarding them. Like maybe they're just taller Smurfs or something.