DPI in Retina iPad app design

The DPI of your Photoshop file does not matter. You can go into Photoshop and change the DPI to whatever you want. Going from non-Retina to Retina is "sort of" like doubling your DPI, however.

If you've already created a design assuming a 1024x768 resolution for the iPad, you will need to recreate the design to at 2048x1536. Where the concept of dpi comes into play is that the density of data should remain consistent at both retina and non-retina resolutions. You'll just need to recreate each bitmap-based element in your file at 4 times the resolution you originally had if you start with a non-retina file. It is sort of like going from 72 dpi to 144 dpi.

You are right.

In a PSD, the DPI is not significant as it only serves to the system to determine how to print the file.

You can always change your PSD's DPI setting to make them happy :) That's definitely not significant.

If set to 264 DPI, a 2048*1536 printed image will be exactly iPad-sized.

And similarly a SD 1024*768 image set to 132 DPI will be same size.

DPI/PPI makes no difference when you're working for a screen, it's the amount of pixels on the screen that matter. If you design for iPad at 2048x1536px at 264ppi or 72ppi, it's still 2048x1536px in both cases. The only difference is if you full size the preview in photoshop.

PPI = Pixels Per Inch. If you're dealing with inches, PPI matters because its the density of that size. If you're measuring the document/canvas size by pixels, then the density would be "Pixels per Pixel" and that's just ridiculous.

Just make sure you're designing at accurate or higher pixels so they can be shrunken if needed for older iOS devices, low res Androids, desktop web, etc.