I don't know of anyone one in the Computer Graphics or Monitor Industry that refers to resolution in the Pixels per Inch or Pixels per CM, frame of reference.
if we are specifically discussing the PPI or PPCM then we discus it as Pixel Density.
and it is a calculated value based off thephysical measured Width and Height of the Screen or display, and it's Resolution in Pixels.
this is Pixel Density or PPI - PPCM
it is the computer graphics industry wide standard, that the Term Resolution, simply means the number of Pixels in Height and Width.
Display Resolution - How many Pixels width and how many pixels height
https://en.wikipedia.org/wiki/Display_resolutionInternet Stats - Width and Height
http://gs.statcounter.com/screen-resolution-statsthis is the computer Industry accepted definition of resolution.
this is a different reference
Pixel Density - this is what you are referring to in your definition of resolution.
https://en.wikipedia.org/wiki/Pixel_densityDot Pitch
https://en.wikipedia.org/wiki/Dot_pitchSo yes there can be some ambiguity when using the term Resolution.
but it is common among computer graphics and Monitors that resolution simply refers to the Width and Heigth in Pixels.
Now when I work in Graphics programming...
There is a big Difference in displaying an image that is 200 pixels x 200 Pixels Square, than there is in displaying an image that is 1 inch x 1 inch square.
Two totally different sets of equations or Graphic routines.
One is based off resolution. that uses just the Pixels width and Height of the object..
The other is based off the target Screens or the displays PPI or PPCM
Also, many displays have a different Vertical Pitch than their Horizontal Pitch.
This too has to be known when dealing with displaying an Image is Actual Size on a target Screen or Display.
Then we can get into Printing and Plotting, which is another different set of technologies.
where resolution takes on a different meaning.
take a look an any monitor supplier of Tv suppliers Site, and check the Specs..
Resolution is Pixel Width and Height