Video jargon can quickly get complicated. But the basics of video are comparatively simple and easily learned, and the rest can follow from that.
C4K, also known as DCI 4K, is 'true' 4K in that it has a horizontal resolution of 4,096 pixels, which is just a little over 4,000 (4K). Almost all 4K video actually shoot 4K UHD, which has a horizontal resolution of 3,840 pixels, a little way below that 4K resolution. C4K sounds more desirable, but the complication is that it's slightly wider than the 16:9 aspect ratio used by other common video standards (including 4K UHD).
The ability to shoot C4K as well as 4K UHD is found on many more advanced cameras, and often seen as a desirable feature, though the additional horizontal resolution is small and the wider aspect ratio could prove an inconvenience. In the world of cinema, however, aspect ratios wider than 16:9 (often much wider) are common.
The aspect ratio of an image is the ratio of its width to its height. The larger the ratio, the ‘wider’ the image; the smaller the ratio, the ‘squarer’ the image.