What changes is that in a tie game at home and the game gets to the 9th, there's no save to be had. You bring in your best available reliever for the 9th; once he is done,, you go with your next best, etc.
As I wrote above, in the postseason and especially in an elimination game, the "rules" should not apply. If your on the road and you don't score, in the top of the 9thor later, you've got to get 6 outs to win the game, the home team doesn't have to get any. Yo have to prolong it as long as you can.