I read everywhere that resolution is defined by the number of pixels on a screen.
But if you imagine 1000 x 1000 pixels on a screen the size of 20 skyscrapers and compare it to 999 x 999 pixels on a box of matches, the resolution would make the skyscrapers screen look 'low-res' and the box of matches screen look 'high-res'. Instinctively, I would say that the box of matches screen is higher resolution than the skyscrapers screen.
Am I wrong to say this? Is resolution definitely defined by the total number of pixels instead of the dots per inch?
Indeed, in the context of displays, the term resolution says nothing about pixel density. As stated in Wikipedia's article on Display Resolution:
The term "display resolution" is usually used to mean pixel dimensions, the number of pixels in each dimension (e.g. 1920 × 1080), which does not tell anything about the pixel density of the display on which the image is actually formed: broadcast television resolution properly refers to the pixel density, the number of pixels per unit distance or area, not total number of pixels. In digital measurement, the display resolution would be given in pixels per inch (PPI)