2K resolution should be 2048×1080, which is the resolution of the cinema DLP chips TI has in the largest 3-chip DLP projectors. Here is an example of one:
https://www.projectorcentral.com/Digital_Projection-LIGHTNING_35HD.htm
4K is 4096×2160 and Sony has a working 4K projector, althought the last I heard the only way to feed it was with 4 HD-SDI inputs and each one gets one quadrant of the image so it isn’t exactly ready for prime time.
There are some other high resolution units out there, like JVC’s QLA-QX1 that is 2048×1536 – basically a 2K width 4:3 projector, but generally 2k/4K is referring to the width and they are now usually a 16×9 projector with an anamorphic lens turret to provide for all the necessary aspect ratios. Prior to this generation of projectors, the cinema DLPs were 5:4 aspect ratio 1280×1024 units with anamorphic lenses.