Difference between when and while?

It's the difference between a point in time and a length of time. "Push this button when the dial reaches ten" means that you watch the dial and at the point in time that it reaches ten you push. Then you can stop any time you like. But if you say "Push this button while the dial is at ten" then when the dial reaches ten you push and you keep pushing until the dial stops being at ten.

"While" suggests that the passage of time for the two events is the same. "I could have written a book while you were in the bathroom." means that the length of time you were in the bathroom is the same as the same as that needed to write a book. "I was in the navy while George VI was king" means that your stint in the navy was coextensive with King George's reign, but "I was in the navy when George VI was king" means that your navy stint was at some time during his reign, but with no implications as to the length of the stint.