2K
Before "4K" became common, you'd almost never see "2K." It was pretty much just a cinema resolution, which is why you'll sometimes see used to refer to a "master format." Most digital cinema projectors used in theaters are 2K resolution (some are less). It's 2,048 pixels wide, and again, no vertical resolution is specified by the DCI.
But now that "4K" has gained traction as a term used to describe TVs and content, "2K" is becoming increasingly common as shorthand for the 1080p resolution used by most HDTVs, as well as Blu-ray. It's not technically accurate, but that didn't stop "4K" from becoming more popular than UHD.
1080p or Full HD
Remember how we talked about digital cinema resolutions only specifying the horizontal resolution?
Well, TVs, on the other hand, have historically used the vertical to describe resolution (going back to the glass tube days). So 1080p is the vertical resolution. Nearly all HDTVs have an aspect ratio of 1.78:1 (16x9, aka "widescreen"), so that means a horizontal resolution of 1,920 pixels (1,920x1,080).
This is another source of confusion, since decades of TV discussions have talked about vertical resolutions, and then all of a sudden we're talking about "4K TVs," which refers to the horizontal resolution. Don't blame me, it wasn't my idea.
That means 1080p is not "1K." It's 2K, as much as UHD TVs are 4K. Which is to say, at 1,920x1,080 they're close to the DCI's 2K specification of 2,048. That said, most people don't call 1080p 2K; they call it 1080p or Full HD.