It's confusing, because 4k has been used as a term (not actually that often in practice) in the VFX industry for 5/6 years for the following resolutions:
4096 × 2160 (standard)
4096 x 3112 (super 35)
Then for 4k cameras, the following resolutions have become fairly common for "4k":
3840 x 2160
4096 x 2304
so these days, it's difficult to know what's been talking about...
What's even more confusing is that after we've settled that 3840x2160 is 4k, which is 4x the pixels of 1920x1080, just like 8k is 4x the pixels of 4k, instead of calling 1920x1080 "2k", everyone is starting to call 2560x1440 "2k", even though 4k is only ~2x the pixels of 2560x1440.
I actually prefer UHD being promoted, because I wouldn't want us to switch to another weird resolution now, and I want videos to just scale up perfectly.
Actually, I've seen 2560x1440 called "2.5K" (at least Blackmagic calls it that in their Cinema Camera which shoots 2432 x 1366), since 2K has a well established definition of 2048x1080, or some crop of that to meet a desired aspect ratio. In film, 4K is defined as 4096x2160, which is exactly 4 times the number of pixels as 2K.
4096 × 2160 (standard) 4096 x 3112 (super 35)
Then for 4k cameras, the following resolutions have become fairly common for "4k":
3840 x 2160 4096 x 2304
so these days, it's difficult to know what's been talking about...