Redemption

A. Verbs

exagorazo a strengthened form of agorazo, "to buy" (see agorazo under BUY), denotes "to buy out" (ex for ek), especially of purchasing a slave with a view to his freedom. It is used metaphorically

lutroo "to release on receipt of ransom" (akin to lutron, "a ransom"), is used in the Middle Voice, signifying "to release by paying a ransom price, to redeem"  

Note: While both exagorazo and lutroo are translated "to redeem," exagorazo does not signify the actual "redemption," but the price paid with a view to it, lutroo signifies the actual "deliverance," the setting at liberty

B. Nouns

lutrosis "a redemption" (akin to lutroo), is used in the general sense of "deliverance,"

apolutrosis  a strengthened form of lutrosis, lit., "a releasing, for (i.e., on payment of) a ransom."

The above is taken from Vine's Word Studies.  (see here)

It is clear from a survey of the new testament scriptures relative to the redemption and ransom effected by the death of Christ that the focus is sometimes upon the act and time when the payment was made (when Christ died) and sometimes upon the act and time of the actual release of the slaves and prisoners.  Christ paid the price for redemption when he died.  The payment guarantees that the release of the prisoners and slaves be effected.  This is definite atonement/redemption. 

When a sinner is released from his captivity in sin (delivered), in the work of conversion, it is also called redemption.  Yet, this is not the time when the payment is made but is what results from the payment having been made.  Not only do the scriptures speak of redemption as occurring when Christ died, and when sinners are converted, but also speak of the resurrection of the just as the "day of redemption."  (Eph. 4: 30)  It is the time when believers shall experience the "redemption of our body."  (Rom. 8: 23)   This is the time when believers will be "delivered from the bondage of corruption."  (vs. 21) 

Thus, there are three distinct aspects of redemption pointed to in Scripture.  First, there is the time of the actual payment of the price of redemption when Christ died.  Second, there is the time when release is first experienced in conversion.  Third, there is the time when full release is experienced at the return of Christ.