All I can say is when you are making something for printing then you will have design measurements in inches. Like when I make a business card I generally ask the client what card size he wants to use and the layout (potrait or landscape). I then use those measurements in inches.
But when I am working for computers....like say website, then I go by pixels. I ask the client what resolution he/she is targetting. If they don't have an idea then I ask them what kind of designs they like? Wide ones or short centered ones. For wide ones you can set the width to 1000px and for short ones to around 780px wide.
You monitor can support different resolution modes (640x480, 800X600, 1024X768, 1200 X 800 for wide etc). I generally test my designs in 1024X768 & 1200 X 800. If designs look fine in these then they will pretty much look good in all others.
I have tried to explain it a bit using example from my experience.
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