Why is digital cinema resolution different from television resolution?

With the advent of cinema grade digital projectors and cameras, we now have standards of digital cinema resolutions such as 2K and 4K. These are similar to high definition TV resolutions (720p, 1080p) but are just measured differently. But how and why?

Up and down vs. side to side.

A TV resolution of 1080p signifies a standard pixel array of 1920×1080. The 1080p term is derived from the vertical pixel count 1,080 (and the fact that it’s progressive scan). The cinematic standard 2K has (approximately) 2,000 pixels across horizontally. This is the inherent difference in measurement between TV and Cinema. TV is measured in a vertical pixel count, while Cinema is measured horizontally.

A 1080p resolution of 1920×1080 is almost the size of a 2K resolution of 2048×1080, it’s just that a different dimension is chosen to express. But why? Why so different?

Genealogy.
A TV signal has always been “measured” vertically since it’s beginning when it was a composition of scanlines. Horizontal rows of info, interlaced together to form an image. When the image processing became digital, it was natural to refer the the number of rows of pixels in place of scan lines.

Cinema, on the other hand, is based on film and size is measured physically as the width of the filmstrip (i.e.35mm) It’s my assumption that with the conversion to digital, filmmakers switched from referring to their media as 35mm (wide) to 2,000 pixels (wide).

So even though both sources use essentially the same medium (digital pixel arrays) their history has lead them to standardize in different ways.