JKSM is an app you install with FBI or run through HBL that basically has you choose the game save you want to edit and edit it on the spot, no need to backup and restore your save or anything. You don't even need a computer, just load up the app, choose the game version you want and you can do things like gen Pokemon in your boxes, clone anything you want, inject mystery gifts (and even multiple copies of them with no problems) or special events (eg: ALL Pokemon XD events legit straight to your box), have an offline PokeBank and so on. As for PGL, it's Pokemon Global Link, that site you need to register on to use things like ranked battle spot battles, online competitions and so on.
https://3ds.pokemon-gl.com/
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I think starting a new game fixes it since it unregisters your game from PGL (it changes your unique Game-ID that PGL uses), which is also why new save files can get another copy.