Jesus is God. He is the same yesterday, today and forever. (Hebrews 13:8)
He is the very same God that He revealed to us in the Old Testament.
Many people, due to their misunderstandings of God's dealings with people throughout history, deny this thus demonstrating their ignorance of the very reason Christ came in the flesh.
Someone once said: God has divided history into "dispensations" or time periods. Each of these in turn has its own special message which Almighty God wants to be dealt out or dispensed to them.
Owing to space constraints, I will outline but three of these dispensations (though I nearly hesitite to use the word due to the negative bias that people associate with it)(which will be called Covenant of XX) below.
God chose Abraham to be the founder of a special people, Israel. This dispensation, called the Covenant of Abraham, began with Abraham. Israel was to be as an example among the nations, showing to the world the true God.
God gave them the law to show them and the world His standard. Since His standard is Himself, that standard is nothing less than perfection. This shows us how holy God is and the penalty for willfully refusing to trust and obey Him reflects how seriously He detests sin. Hence we read of His judgment on sin with the destruction of Sodom and Gomorrah, with the flood, of the sinful races that practiced widespread sin such as the Amalekites and the Amorites, etc., but not after He had mercifully warned of His impending wrath for hundreds of years to give them a chance to repent.
Humanity has proven throughout history that we are simply incapable of keeping God's commandments. We needed a Saviour, someone that could fulfill the law flawlessly. Logically then the only one who could keep God's law was God. This reminds us of His desire for us to trust and rely on Him alone for everything in life. God told us He would save us from sin from the beginning since sin first appeared. This Saviour was to be the Word, the Son of God who became the Incarnate God and was named Jesus.
Jesus' ministry on earth was lived under the period of the Law which, known as the Covenant of the Law, began with Moses and ended with John the Baptist: The law and the prophets were until John. Luke 16:16 . It was for this reason that Jesus, when asked what one should do to have eternal life, gave the answer, 'Keep the commandments.' (Matthew 19: 16 - 17). Hence it will surprise many here to know that many scholars have said that the books of Matthew, Mark, Luke and John are in the main, Old Testament, or Old Covenant books.
Only during His last 72 hours on earth did Jesus introduce us to the New Testament, or New Covenant, through His shed blood. Jesus, who is the same God of the Old Covenant or the Old Testament, Himself said that He had not come to abolish but to fulfill the law and the prophets. (Matthew 5:17) Here an understanding of the world 'fulfill' is essential. Jesus came to fulfill the law, that is, to bring about the completion or achievement of the Law. And what is the achievement of the Law? This: the Law demonstrates to us our need of a Saviour because we are incapable of keeping God's commandments and will always fall short of God's standard. Our need of a Saviour is fulfilled in Jesus Christ. Hence Jesus came to earth not as a judge of the nation of Israel, or to execute judgment on sinners according to the Law, but to offer God's plan of salvation.
However, this plan of salvation was rejected by the Jews when they rejected Jesus as their Messiah. The Jews were expecting their Messiah to come as conquering warrior king like David, (because they failed to understand that Scripture revealed that Messiah would be coming two times for two different purposes, first as Saviour, second as Conqueror) but what they found in Jesus was not a lion but a lamb. Because they refused Jesus as King, the message of salvation then came to the non-Jews- the Gentiles. Christ was 'made sin' and took upon Himself the sins of everyone. According to Romans 11, this was extended to non-Jews because a blindness in part has been put upon the Jews until the fullness of the Gentiles come in and then all Israel will be saved.
Hence was ushered in a new covenant.. the Covenant of the Grace of God. This was a mystery that was not revealed during Jesus' earthly ministry. It was only revealed after His death and resurrection and the revelation came to Paul who spoke through the Holy Spirit. (Acts 20:24) God's grace period will last until the last non-Jew is saved, then comes the deserved wrath of God upon an unbelieving and rebellious world shortly followed by Christ's Second Coming in glory to mete out final judgment. For we read in Revelation and the prophets of the Old Testament that, shortly, Jesus will return as a potentate, and He will judge the world as He did in the days of Sodom and Gomorrah, of Noah and of Jonah, et. al., and He will re-claim the world as all the kingdoms are restored to Him.
Let us pause for a moment and let this sink in:
Because of Jesus and His sacrifice on the Cross, there was no longer any need for the former punishments and 'slaughters' under the Law as Jesus would be the One who would bear everything everyone ever deserved. This is the whole point some people who compare how God dealt with people under the Law and now under Christ's grace miss.
Many will not accept this fundamental truth. Indeed, since it is so fundamentally straightforward, based on what the Scripture says, those that do not want to believe (as opposed to 'cannot') will simply label the messenger as a 'fundamentalist' as if this is somehow a bad thing, and deny, deny, deny.
Scripture is clear, with quotes from the Old Testament, YHWH being attributed to Jesus in the New Testament, making it very plain that they are one and the same God. (e.g. John 12:39-41 with Isaiah 6:1-3; Hebrews 1:10-13 with Psalm 102:25; 1 Peter 2:4-8 with Isaiah 8:13-14 )