So it uses two sets of resolution at the same time?
Sort of... Applications that don't know about HiDPI mode will see the screen resolution as whatever you set in the Monitors control panel. Applications that know about HiDPI mode can access the full resolution of the display. Much of the UI will take advantage of it even if the application doesn't know about HiDPI.... menu text, dialog buttons, etc that are actually drawn by the OS are drawn at the higher DPI.
For example, the Finder on a traditional display might display a 32x32 pixel icon for a file. On a retina display, it draws it using 64x64 pixels, but it occupies the same size on the screen.
What about ipads and iphones? How would one go about desiging a website for them if they claim to have these enormous resolutions that aren't their actual resolutions?
Google for HiDPI Web Design. You'll find out how to code a site to take advantage of the hi resolution. Basically you'll need two images. One is standard resolution for standard displays, another is double the size, X and Y. The hi resolution image will take the same amount of the page, but it will be much sharper and criper for those devices that support it
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I'm more concerned though with the design of the site itself. I'm new to thist stuff and thought I had a handle of it just assuming any browswer/screen wider than 1000 pixels would mean desktop/laptop and could use a regular website design. But if iPads really do have these enormous resolutions you can't make that assumption and will need to have the mobile version displayed even on 1000px and larger screens.