Actually, display resolution refers to exactly what you call pixel density, and NOT the pixel dimensions. This error is so common that the term resolution has practically been redefined outside of the professional (science and engineering) space, but technically, display resolution and pixel density are the same thing.
It is double the resolution, because resolution is expressed as an x,y pair. It is 4 times the pixel density for the same screen size.
Actually, display resolution refers to exactly what you call pixel density, and NOT the pixel dimensions. This error is so common that the term resolution has practically been redefined outside of the professional (science and engineering) space, but technically, display resolution and pixel density are the same thing.