You can definitely export the project to something like PSD for work later in Photoshop *but* you must use a file service like Dropbox (or Creative Cloud). (And if you do work in Photoshop, you must save as PSDX (PS Touch's native format) if you intend to do further work in PS Touch, otherwise PS Touch will flatten an imported plain PSD file.)
Otherwise, you'll have to deal with file formats like JPEGs and PNGs if you intend to do everything locally.
So, it sounds like if I was to save as a JPEG or PNG (without layers, I know) I can save these to a folder on my tablet, and if I want to, copy them to a flash drive or SD card.
But I'm not clear about what you're saying: about the other file types: it sounds like I can save them on my device as either PSD or PSDx, but the only way to get them off the device is via the creative cloud, or a site like dropbox? Why couldn't I save as PSD/PSDx and then copy to a flash drive/SD card, as I would a JPEG file?
that's confusing. Best, David.
PS Touch contains your projects in an organizer within the app itself. These are (I'm assuming) PSDX files until you export otherwise using the "Share" or "Save to Gallery" option. (Referring to Android; it might be slightly different on iOS.) Depending on how you export will determine what file types are available. (e.g., You can save locally to your device as JPEG; PSD to Creative Cloud or Dropbox.)
Why it's done that way? Not sure. Maybe because of file size issues. It would be sort of redundant to have the PSD file on your device when the same project in PSDX format already exists in PS Touch itself.
On iOS you do have an export option "Copy to iTunes" allowing you to choose jpg, png and psd as export formats.