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 4K UHD standard doesn't specify how large the pixels are, so a 4K UHD projector (Optoma, BenQ, Dell, et al.) counts because these projectors have a 2718×1528 pixel structure. Those projectors process the true 4K of data and project it with overlapping pixels, which is what pixel shifting is. Unfortunately, each of those pixels is far larger: each one has 50% more area than true 4K. Pixel shifting projectors project a pixel, shift it up to the right, by a half diameter, and project it again, with modified data, but that second pixel overlaps the first.