I'm still confused though. In your desktop monitor analogy, although the monitor size did not change, the resolution did, as in 1920x1600 to 2560x1600 - hence you can see more of the webpage. Is this not comparable with 720p to 1080p? Aside from pixel density, going from 720p to 1080p also changes the resolution right?
Correct, it is comparable to 720p -> 1080p. The resolution has indeed changed, but your viewport (the phone screen, or the monitor in this case) has not changed in size. It's displaying more information in the same amount of space.
For example, please look at my forum avatar.
It is a 50 x 50 pixel square. Your monitor right now no doubt has a much higher resolution than that, therefore, you can see it and a whole lot more information around it.
However, if your monitor only had a 50x50 pixel resolution (and was a square, for some unknown reason) this avatar would occupy the entire space on your screen, and would wind up being huge.
To demonstrate this simply, view this web page, or any web site, or image. Then lower (or increase) the resolution on your monitor.
How much information is displayed to you, and thus how "big" or "small" the web site now looks has changed, but your monitor's physical size did not.
Hope that helps. If it's still confusing, send me a PM and I'll draft up an image for you.