As a matter of fact, the nature of Jesus mission was not really different from that of Old Testament. His mission was following the law of God as he preached and called people to repent.
“From that time Jesus began to preach, and to say, Repent: for the kingdom of heaven is at hand.” (Mathew 4:17)
“14 Now after that John was put in prison, Jesus came into Galilee, preaching the gospel of the kingdom of God… 38 And he said unto them, Let us go into the next towns, that I may preach there also: for therefore came I forth. 39 And he preached in their synagogues throughout all Galilee, and cast out devils.” (Luke 1:14-39)
“43 And he said unto them, I must preach the kingdom of God to other cities also: for therefore am I sent. 44 And he preached in the synagogues of Galilee”. (Luke 4:43-44)
We note here that Jesus said explicitly that he came only to call people to repent which is the way to salvation according to the Old Testament. The idea that Jesus came to redeem people and die for their sins to be forgiven was not said explicitly by Jesus. It was only mentioned in the wings of Paul.
“21But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets; 22 Even the righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: for there is no difference: 23 For all have sinned, and come short of the glory of God; 24 Being justified freely by his grace through the redemption that is in Christ Jesus: 25 Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God;” (52-Romans 3:21-25)
“17 For if by one man’s offense death reigned by one; much more they which receive abundance of grace and of the gift of righteousness shall reign in life by one, Jesus Christ.) 18 Therefore as by the offense of one judgment came upon all men to condemnation; even so by the righteousness of one, the gift came upon all men unto justification of life. 19 For as by one man’s disobedience many were made sinners, so by the obedience of one shall many be made righteous”. (52-Romans 5:17-19)
Paul did not stop here; he added that believing in Jesus would wash away all their sins and there will be no condemnation for them.
“1 There is therefore now no condemnation to them which are in Christ Jesus, who walk not after the flesh, but after the Spirit. 2 For the law of the Spirit of life in Christ Jesus hath made me free from the law of sin and death.” (52-Romans 8:1-2)
Did Jesus really come to redeem people with his death?
To answer this question, we have to study the nature of the acts of Jesus during the time of his life on earth which can be summed as follows: