As a general rule, when your working on a screen, forget about physical dimensions and resolution (PPI). All that affects the size you see something on screen is its pixel dimensions. Your screen doesn't know what an inch is, all it knows is pixels.
In your examples:
- 1×1 inch image at 72PPI is 72×72 pixels.
- 1×1 inch image at 27PPI is 27×27 pixels.
Your screen shows those images at their pixel size, ignoring any physical dimensions or resolution settings.
If you were to print those images they would both print at 1 inch square. The only time the resolution really comes in to play is when you print.
If you were to import your images in to say InDesign, they would both show at 1x1 inch because InDesign is resolution aware. This is because InDesign is made for (or at least was traditionally) print design—where resolution really matters.
Your screen's resolution (as are most screen resolutions) 72 ppi. If you change the resolution to be higher, it will appear larger on your screen to achieve the same visual "density" if you will. Likewise, when the resolution is lower, it will appear smaller.
Allow me a metaphor.
Imagine you cover 1 sq. inch with 72 cheerios and you are looking at it from 3 feet away. Now imagine you remove cheerios till you are left with 27 cheerios, but those cheerios have taken on milk and are much larger to fill the space. In order for those cheerios to appear the same size as the 72 did before, you have to look at it from further away. Thus, the smaller square.