To redeem is simply to buy back or recover ownership. To better understand this, if your car is impounded for unpaid tickets, you can get it back, or redeem it, by paying the fine. In this sense, Jesus redeems us from our imperfect state for God.
As such, Jesus acts as our redeemer, that is, one who redeems.
Redemption is the act of redeeming someone (see reconciliation).
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