4K resolution
As noted above, DCI 4K is 40962160, while 4K UHD is 38402160, producing a slight difference in aspect ratio rather than a significant difference in resolution. Traditional displays, such as LCD or OLED, are 3840 pixels across the screen, with each pixel being 1/3840th of the screen width. They do not overlap—if they did, they would suffer reduced detail. The diameter of each pixel is basically 1/3840th of the screen width or 1/2160th of the screen height - either gives the same size pixel. That 38402160 works out to 8.3 megapixels, the official resolution of 4K UHD (and therefore Blu-ray UHD discs).
4K resolution
The main advantage of recording video at the 4K standard is that fine spatial detail is resolved well. If the final video quality is reduced to 2K from a 4K recording, more detail is apparent than would have been achieved from a native 2K recording. Increased fineness and contrast is then possible with output to DVD and Blu-ray. Some cinematographers record at 4K with the Super 35 film format to offset any resolution loss that may occur during video processing.