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
Pixel shifting, as described here, was pioneered in the consumer space by JVC, and later in the commercial space by Epson. That said, it isn't the same thing as "true" 4K. More recently, some DLP projectors claim 4K UHD (which the JVCs and Epsons do not claim).