With your examples of Pages and other apps, the files they save are sandboxed and stored within that app's package. Technically it's the same, but note that you can't get directly at them. You can print your Pages document to an AirPrint capable printer, but what else? I'm not even sure you can get that file off the iPad to a desktop computer.
I played with Preview and the Adobe Reader a bit in iOS 8 (where I'm typing from). I can easily view PDF files from the web, but can't do much of anything else with them. The Reader has an Edit button (haven't tried that yet), but then I'd be at the same point. Where and how do I save the edits?
Edit: Scratch that. The Edit button in the Adobe Reader doesn't have anything to do with actually editing the contents of a PDF file. You select PDFs that are on the iPad and decide what to do with them (delete, rename, create and store them by different folders). One option though is to send them to your Adobe account at an Acrobat.com storage space. Then you can pull the PDF back down to your desktop computer. But you still can't create a PDF out of anything. At least, not that I can see. If you had a way, I think that's where the Reader comes in. It finds any PDF files on your iPad and displays them in a list. If you could create one, then you could send it out through the Reader.