Does the image file I submit to deviantART have to be the same file I submit to Prints?

No, not necessarily. But when you submit a deviation intending to make it available as a print, you can initially upload a hi-res print source image to the file deck and resize it in the deviation submission process for deviation display.

In any other case, they should most definitely be different:

Images for display on deviantART (deviations) should be saved at lower resolutions/file sizes since they will be viewed on screen only.

Images submitted to Prints should be at a higher resolution that is more suitable for printing and should not contain any watermarks. This high resolution file will not be available to the public.