There are several 4K cameras out there. Remarkable though they are, what the manufacturers mean by “4K” needs some interpretation and explanation.
The practice of using a number followed by a K as a shorthand to indicate resolution originated in the world of film scanning. Achieving high resolution scans frequently means a line-array sensor, a CCD imaging sensor comprising a single strip of photosites per colour channel, with either the film being moved past the sensor (as in a Spirit datacine) or the sensor being moved past the film (as in Filmlight's Northlight scanner). Other scanners use area sensors, but given the ability to sample slowly, at several frames per second, and to use sequential RGB exposures, the result of both these approaches is that every pixel in the output image has carefully-measured levels of red, green and blue in it, based on the information on the film.
At about the same time film scanning was becoming really good, so was digital still photography. The desire to achieve a similar form factor to traditional DSLRs, and to use their lenses, make it necessary to find a fairly direct replacement of film, with a single sensor capable of capturing a colour image. Low-cost colour video cameras had for a long time been producing workable results with a single sensor patterned with red, green and blue filters, with the missing values for each colour channel interpolated with varying degrees of sophistication. Such sensors in digital stills cameras were and are characterised with the familiar megapixel count; the number of millions of photosites on the sensor.
Dalsa got there first
So far, so obvious, but the argument about resolution is based on a mixing of this terminology. Despite popular prejudice, it wasn't actually Red who started doing this. The first people I remember referring to a single-chip motion picture camera as being of 3K resolution were Dalsa, with their seminal Origin digital cinema camera. In my view, this was (and, if you aren't a cultural relativist, remains) a fundamental misapplication of terminology; using a term customarily used to describe one process to describe a completely dissimilar process, and perhaps not coincidentally doing that with an eye on the commercial advantage.
It's not my intention to in any way criticise the performance of the Dalsa Origin. It was, and even now would still be, an absolutely superb camera, easily the best available at the time in terms of sheer information in the image, and I'm sure the company would remain at the head of that particular pack had they chosen to continue in the field. But was it fair to describe it as 3K? I don't think so, no matter how clever their algorithms were. OK, fine, the algorithms can be clever. Mathematical procedures for recovering full RGB data from a Bayer filter array camera can be sophisticated, and can often achieve results on certain types of image that appear to defy the assumption that two thirds of the output image is interpolated, generated, or in some way made up.