Thanks for prompting me to look it up I now understand that the apps take care of the post-processing but you are still basically taking a photograph so my main point still applies.
Basically a flat bed scanner simply takes a photograph and the post processing is done on an attached computer. There are few scanners that will provide internal storage or post scan facilities.
I have some limited experience of photographing pictures and documents, and have found that corrrect lighting is the single most important factor. Beware of reflections from windows, etc.
Correct lighting is at the heart of any photography and Control of the lighting environment is of paramount importance. Part of the functionality of some of these Apps (but not all) is to even out the light striking the subject and to provide a suitable light level.
An ideal scenario for copying old photographs and documents would be a fixed focal framework for the camera and a light tent around the subject to provide the correct diffuse light level but this isn't always possible. The next best thing (in my opinion) is a very good quality scanner - but again this isn't always suitable (books with stiff or fragile spines) and other means have to be brought to the fore.
The use of a mobile phone or tablet computer for this purpose would have seemed ludicrous a few years ago but with the advances in the technology they are now a viable alternative as (in my opinion) a mobile alternative- although like all compromise solutions they are not perfect.
It is of course possible to simply use the camera as a camera but the added functionality of some of these Apps is to provide the added functionality of a graphics program for post scan production work - some Apps go further - for example one allows a scan of multiple images on a page to be split automatically into the separate images.
Another advantage as a mobile solution is that you can immediately see the results and if they are not satisfactory redo them