The size/resolution of your screen and the size/resolution of the perceived image are not relevant to each other - I think that might be part of the perceived distortion problem.

Go to Image>Image Size, and change the Document Size section to show you the size in inches or centimeters (whichever one you use for measurement), and THAT will give you the dimensions it will print out.

An 800x800 pixel image will be nice and big on your screen, but printed out at 300dpi (if that is what it is set to) you will have a 2.66x2.66 inch print - teeny-tiny! If it is set to 72dpi, then you will have an 11.11x11.11 inch print - and a lot of times your printer (the HP) will know it is the wrong size for the paper (meaning you're usually printing it on an 8.5x11 inch sheet) and "squeeze" it to fit so you end up with a distorted image.

Does that answer your question? hope that helps-
-Lew ;-)