WONKO'S IMAGE SIZING TUTORIAL
CONCLUSION
Essentially, both ways of representing the size of an image are correct and valid. Some are just simpler in some circumstances than others to work with.
To summarize what happens when you change one figure in the equation:
Or for the mathematicians:
P = R x D
where P equals the pixel measurement, R equals the ruler measurement, and D equals the dpi.
(Don't let the math scare you. If you got it before that, you most likely had it correct.)
Anyway, in my humble opinion, you are in most cases better off if you use the pixel measurements. This will minimize the possibility of sizing errors and confusion. Using that as your base, you will soon be able to work back and forth from dpi to pixels and feel comfortable doing it.
Good luck!