An excellent point. It for this very reason that Imperial German medal collectors will talk of "Original Issue", "Period-Made" and "Spangenstück" "after war issue" etc. It makes a difference, however all may be "real" there are just valued differently.
The Wurttemberg GMMM issue medals in .333 gold has a value well over $1,000, however the Spangenstück made for the medal bar is not precious medal and is valued much less.
An opposite example is the Prussian or Bavarian Pilot badges. The wartime issued cliché ones sell for a fraction of the post-war Junker or Poellath made ones.
Your issued medals are original. The medals you buy online are original. Your issued medals are attributed to someone (you). The ones you buy online are not. If you buy extra medals to wear on a second suit or uniform they become attributed to you. Years from now if your family sells your possessions, a collector could buy your group of medals. He would display your original issue medals and your extra set. Both sets would be attributed to you.
To your other point;
Your mother's print of the Flemish master is a copy. It is beautiful and depicts the image as well (or better) than the original, but it is still a copy. Another copy can be created. There is only one that the painter made. Even if he tried to paint two identical portraits, it would be impossible not to have some subtle differences. Like any other copy of an art piece, even if it is executed in the same perfect style, the copy will not command the same price as the original.
Originals represent the moment in time that they were created and uphold the truth of the piece. Both the pluses and the minuses.