There is reference to God not changing in both the Old Testament and the New Testament:
I the Lord do not change. So you, the descendants of Jacob, are not
destroyed. (Malachi 3:6)
Jesus Christ is the same yesterday and today and forever. (Hebrews
While God has not changed, there are some things that have changed, such as God's dealing with mankind based on the death & resurrection of Jesus Christ.
He is the atoning sacrifice for our sins, and not only for ours but
also for the sins of the whole world. (1 John 2:2)
God has dealt with mankind based on covenants or testaments, so there is a distinction between Jew, Gentile, and the Church of God.
Do not cause anyone to stumble, whether Jews, Greeks or the church of
God (1 Corinthians 10:32)
In the New Testament there is still reference to God being a jealous God:
Are we trying to arouse the Lord’s jealousy? Are we stronger than he?
(1 Corinthians 10:22)
Or do you think Scripture says without reason that he jealously longs
for the spirit he has caused to dwell in us? (James 4:5)
The apostle Paul refers to being jealous:
I am jealous for you with a godly jealousy. I promised you to one
husband, to Christ, so that I might present you as a pure virgin to
him. (2 Corinthians 11:2)
But he states that it is a "godly jealousy".
This is a really big topic, which may raise more questions, but to wrap up what I'm saying, 1 John 2:2 talks about Jesus satisfying God's wrath against sin. That is the difference, we now have a better covenant/testament based on better promises.
But in fact the ministry Jesus has received is as superior to theirs
as the covenant of which he is mediator is superior to the old one,
since the new covenant is established on better promises. (Hebrews