1080p = 2k; both are 1920x1080p. p is rows in the vertical dimension (p for progressive, as opposed to i for interlaced; e.g. NZ terrestrial TV is 1080i). k is columns in the horizontal direction, and comes from film making and visual effects (1920 rounds up to 2k and 3840 rounds up to 4k).
Wow, I didn't know this! I mistook it for 1440p (that's what my monitor is). I figure that it might be between 1080p and 4k that it was synonymous with 2k, but I'm mistaken.
Yes, k stands for thousand. Historically, 4k meant 4096 pixels wide in the context of digitised film or digital visual effects, and 2k meant 2048 pixels wide. TVs ended up 1920 pixels wide, which is "close enough" to use the same term, 2k. I think "4k" is used for marketing TVs as it's easier to remember and say than "2160p", so now we mix the terminology.
Its a loophole. UHD4k is what tv advertiser used to dilute meaning and not get sued. I believe the definition has been diluted to the point 4k is expected to be UHD.
