Both do indeed contain the number 2160, which might be where people are getting confused, but the thing is, for 4k, that number represents the vertical pixel count, and for the Vive, it represents the horizontal pixel count.
- Pixel Count -
Below I have attached a image showing how many pixels a Vive would take up when compared to a 4k screen. The small text, that probably just looks like dots in the image, are "4k" text & "Vive" text, both @ 12pt font size. I have overlayed larger 300pt font just so you know which is which.
PS: I like the Vive, I just don't like it when people claim VR headsets have a 4k resolution.