"4K" refers to horizontal resolutions of around 4,000 pixels. The "K" stands for "kilo" (thousand). As things stand, the majority of 4K displays come with 3840 x 2160 pixel (4K UHDTV) resolution.
(Full) HD hat 1920 x 1080 Pixel.
4K hat zwar eine vierfache Pixel-Anzahl, aber nur doppelte Aufloesung (Linienpaare pro mm).