Christ as Redeemer

I have been studying the encyclicals of Pope John Paul II of late, and it occurred to me this morning that three of his twelve encyclicals refer to Christ as 'redeemer': his first, Redemptor Hominis, as well as Redemptoris Mater and Redemptoris Missio. In our culture, we are perhaps more accustomed to hailing Jesus Christ as Savior. Does the image of Christ change if we call Him 'Redeemer'? 'To redeem' has the sense of 'to make good', 'to restore', whereas 'to save', while not excluding these ideas, perhaps downplays them. When terrible things like Hurricane Katrina or last year's tsunami devastate large groups of apparently innocent people, does Christ as Redeemer help us to make sense of these catastrophes in a way that Christ as Savior might not?