Holy shit, what an episode. I was clenching my fists pretty much all the way through the Hardhome scene. I was already sort of spoiled that the White Walkers would show up, so all week I've been thinking 'if they do show up I won't be surprised, and if they don't I'll be disappointed'. I wasn't exactly surprised, but oh my god did it deliver. And I love every single mention of the Walkers on the show, so this episode was a GoT wet dream for me. And I agree, quite possibly the best episode of the show so far.
The rest of the season might be excellent, but I think it'll be tough to top this one.
The show has referred to them as the Others. That is how various characters who don't believe in their existence have referred to them, or in oaths/curses ("The Others take your worthless hide!").
What I can recall, none of that has actually been used on the show, only in the books.
And the show has referred to the wights as wights a few times, but the last time was in season 2 I think, so that's a long time ago. But they look vastly different, so I don't completely get the confusion.