A complete list of deck concepts would be difficult as there are so many possibilities but at the broadest level, most will probably fit into one (or more) of these categories:
Rush Deck: Basically pure offensive deck designed to kill them before they kill you
Stall Deck: Tries to delay, stop, or simply outheal your opponent's attack until you can either deck them out or achieve a certain winning combination
Burst Deck: Somewhere in between the first 2, these will start off building up slowly, then suddenly drop large numbers of creatures or deal massive damage all at once to quickly finish your opponent off(includes most fractal decks)
Destruction/Denial Deck: Tries to either destroy anything your opponent plays or prevent them from playing it in the first place by destroying quanta sources and/or stealing quanta, preventing them from drawing cards etc.
Mindgate Deck: Uses your opponent's own deck against them