UHD is 4K.
One flavor of it, anyway. And actually the more popular of the two.
4K is shorthand for 2160, which is twice the dimensions of HD (1080) - kinda.
There are two flavors - one for consumer-grade TV, which is exactly twice the dimensions of 1920x1080 HD, i.e 3840x2160, Ultra High Definition, aka UHD 4K, which is the one that's in most TV stores, with the regular 16:9 widescreen format, and
the second one, which is slightly wider at 4096x2160, is a professional format made for cameras and cinemas and is called the Digital Cinema Initiatives standard, aka DCI 4K. This is also exactly twice the dimensions of the current professional 2K standard for digital cinema projection - 2048x1080.
Of course there are thousands of UHD TV's to every one DCI cinema projector, so actually when you say 4K - mostly you're referring to UHD.
HTH