iOS7 Moving Backgrounds - file type and creating your own

You are confusing parallax and dynamic.

Parallax is the name given to the effect whereby a still image is moved in response to input at a greater or lesser extent than other on screen elements, to provide a sense of depth. The image used is just a static image file that is slightly larger than the screen size, to allow it to move slightly without introducing blank areas.

Dynamic backgrounds are the animated ones that move according to their programming, not just your input. I suspect they are simply quartz composer files like an OSX screensaver.

It looks like Apple doesn't specifically allow you to create dynamic backgrounds - but this developer has a demo of one working.

You can use any 'Still' image from your own images or one of your iPhone preset images to be used as a wallpaper. The parallax effect is than applied to that image, so you do not need a special image to get the parallax effect.

Besides the 'Still' wallpapers, you can also choose a 'Dynamic' wallpaper that iOS 7 provides. You can not use your own 'Dynamic' wallpaper.

If you want can turn of the parallex effect in your system settings (it is somewhat hidden).

Settings -> General -> Accessibility ->  Reduce Motion

(Note that the parallax effect is not available on the iPhone 4.)