When I play the Trainer Challenge, I can't pick certain decks that I have available through online battles. In addition to that, I have 3 basic decks that are available in Trainer Challenge that I can't use elsewhere, specifically XY Basic Red, XY Basic Blue and XY Basic Green.
I'd like to know what determines in which mode I can use a certain deck? It probably has to do something with how the deck was acquired, but I couldn't find any concrete evidence to back this up.