2K is supposed to refer to a 2048x2048 square 1:1 aspect image, same with 4K being a 4096x4096 image. This term is correctly used a lot when referring to texture sizes. A 4K texture is 4096x4096 texels.

I think the term started getting mixed up with people discussing what resolutions benefit from texture size increases. Generally, if you are running, say, 4K textures, you would really only always benefit from that if you have a 2160p screen, just because lower resolutions dont have the definition to actually display those texels. So, people start inter changing "4K screen" and "4K-benefitting screen" and we end up where we are now.