What's the definition of 2K?

After the release of the iPhone 6 plus, I'm seeing so many comments such as 'why didn't they put a 2K display in it'.

I was certain that 1080p is 2K, since it's 1920 which is rounded up. The same applies to 3840 - it's 4K (both 16:9).

People are referring to what I thought was sort of 2.5K - 2560x1440

Am I wrong or are others wrong?

2K is a generic term for one of several resolutions: http://en.wikipedia.org/wiki/2K_resolution

4K was an industry standard (4096 x 2160), although the same is happening to it. 4K is being used around for 3840 x 2160 displays, so it'll become another generic term soon enough.