As long as the image remains on the computer there is no need to worry about converting this to some other resolution using some other terminology.
Pixel dimensions work well for Web pages, for example.
The reality is that many images aren't very useful if they remain on the computer. Their real usefulness lies in their transfer to film, video tape or printed paper such as magazines or posters. The trouble with this is that printing an image is much different than simply viewing it on the screen. Printing also requires a different set of dimensions because of the way they work. Printed images are handled by the number of Dots Per Inch that the printer can handle.