Typically, "atonement" is used to refer to the broader scope of the salvation accomplished by Christ's passive obedience
, i.e., His death.
"redemption" is one part of that atonement. It refers specifically to the "paying off a debt owed; to buy back". Probably the most vivid biblical example can be found in the book of Hosea, where Hosea "redeems" Gomer from the auction block. Another example is found in the book of Ruth.