Personally I run two Asus ROG PG278QR 's from twin GTX1080's. Resolution is set at 5120x1440@120hz.
So 1440p @ 120hz.
So for my set up, I only need to get my frame rate up as high as 120. Anything beyond that is superfluous as the screen will only show 120. People who aim to get high frame rates beyond the refresh rate of their screen are only doing it for bragging rights.
As for the original question about the definition...well I am in two minds as if it is even worth it, as generally the human eye cannot see beyond 1k, its starting to feel like a selling gimmick by the big companies...but thats my own opinion.