Who moves first, and who moves last? In a game between the monetary authority and the fiscal authority, the order of moves matters. Just like in Stackelberg duopoly, where the effect of an increase in one firm's quantity will depend on whether the other firm is the leader and has already chosen its quantity, or is the follower and will adjust its quantity in response.
But there is also a Short Run vs Long Run distinction between the order of moves. In the Short Run game, stabilisation of Aggregate Demand is what's at stake. In the Long Run game, satisfying the Long Run Government Budget Constraint is what's at stake.