1080p == 2K

1080p is 1920x1080 and 2k is 2560x1440

What? Who defines 1440p as 2k?

https://en.wikipedia.org/wiki/2K_resolution

I don't doubt it's used that way, but that makes absolutely zero sense.

For that matter, it's 1080p that's half the (linear) resolution of 4k.

2K is a generic term for resolutions that have a horizontal resolution of approximately 2,000 pixels. In terms of cinema the DCI standard for 2K is 2048x1080. There is also the flat cropped resolution of 1998x1080 and the cinemascope cropped resolution of 2048x858. 1080p has the same vertical resolution as DCI 2K and it's horizontal resolution is also approximately 2,000. 2560x1440 is 560 pixels more than 2,000 compared to 1920x1080 which is only 80 pixels away. That is 7x further away from exactly 2,000. Calling 2560x1440 2K is too big of a stretch. If you wanted to give it a name based upon its approximate horizontal resolution then you should call it 2.5K.