I got the impression that all of the White Walker leaders, including the Night King, were what became of Craster's sons after they were left in the woods. These guys are not spoken of in the books - at least, none of the ones that have been published to-date. These things are all new and we readers of the books are on the same footing as those who haven't.
There currently seem to be three, possibly four, maybe even as many as five tiers in the Others' hierarchy. At the lowest rung, there are the Whites - the undead that are killed and subsequently resurrected to fight the living. Then, within the ranks of the "main" Others, we have what I call the "soldiers" - the shirtless ones that go out and collect Craster's sons and occasionally run armies of whites on horseback. The one that Sam took down was one of these. There was another during the Whites' march on the Fist of the First Men. Then, there appear to be "generals" or "officers", like the one we saw take on Jon Snow. A second one appeared on the beach at Hardhome as Jon and the remaining survivors escaped. These might also be the same as the "soldiers" who just happen to be wearing armor, but I'm not 100% sure. Then we have the "royals". These, I think, are Craster's sons. There were many of them present torwards the end of "Oathkeeper", blurred in the background, when the final son was brought in. They all seem to be bald with ice spikes growing out of their heads as stylized crowns and were on the horses at the top of the cliff. Only one of that caste, possibly the eldest/first-born of them, is the "Night's King".
I am truly fascinated by these guys, and I'm hoping this is a major part of GRRM's actual intent for the story progression and not just a construct for the show. Considering the import and seriousness of their growing involvement, I'm pretty sure this was a part of "His Plan" from the beginning.