Yeah, stupid confusing, but when the use a 'k' number (thousands of lines) they are talking horizontal lines, but when they use p or i (progressive/interlaced) they are referring to vertical lines.
It's why UHD/4k TVs are going to be confusing to the public. It almost sounds like it's 4 times the resolution of 1080p, but it's more like double. (Besides the fact that seeing the difference will be nearly impossible.)
My mom still gets confused trying to record one show on her VCR while watching another. I can't even attempt to explain HD.
Oh, and good script, ntcuFaal, I like that. It takes the eyeball out of the equation.