4k refers to approximately four thousand horizontal pixels. 1080p refers to 1080 vertical pixels. So how many 'k' and how many 'p' a display is/has aren't comparable figures.
I know that and 'k' just means thousands, but in context they still indicate which dimension is being referred to. 'p' is never used to refer to horizontal dimension metrics and I've never seen 'k' on it's own with a number used to indicate vertical resolution. Not without that being explicitly stated anyway.