4K resolution
So while 4K UHD sounds like it has a pixel structures with 1/4 the area of 1080p, that does not happen with pixel shifting. Only a true 4K projector offers that level of resolution. That's why "true" 4K projectors cost so much more than 4K UHD projectors with otherwise similar feature sets. They produce smaller pixels, finer resolution, no compromising of detail or color from overlapping pixels. By comparison, the slight difference in aspect ratio between DCI and 3840×2160 pixel displays without overlap is insignificant relative to the amount of detail.
4K resolution
Some 4K resolutions, like 38402160 are often casually referred to as "2160p". This name follows from the previous naming convention used by HDTV and SDTV formats, which refer to a format by the number of pixels/lines along the vertical axis (such as "1080p" for 19201080 progressive scan, or "480i" for the 480-line interlaced SDTV formats) rather than the horizontal pixel count (≈4000 or "4K" for 38402160).