Resolution-wise, 2K is 2048x1080 and 4K is 4096x2160 pixels. The 2K and 4K standards are authored by the Digital Cinema Initiative: 2K-compliant systems must support 24 or 48 fps, 4K-compliant systems must support 24 fps. They don't take account of common LCD sizes since they're a projection-based standard using TI DLP technology which is manufactured by Barco, NEC, Sony and a couple of others. A while back Sony had the only 4K projector, I don't know what the situation is now.
Incidentally, a 2K image (and HDTV) is only 2.2 megapixels if you do the math.
The standards allow end-to-end digital delivery of content. Movie prints cost $25,000 or more each, so they can be a bottleneck for smaller theaters trying to get ahold of a blockbuster print. This is why, in the past, the UK tended to get US movies later than Europe: European countries needed subtitled or dubbed prints, so they got new prints. UK could go with prints that had already been show in the US. Digital stuff can be delivered over wire or on hard drives (400GB): duplication costs are effectively nil. This lets a theater assign screens on the fly if there is unexpected demand (or lack thereof) for a movie.
Anyway, none of this helps Mr Draper, who probably needs a cord of good quality logs for his player's boiler.