Are there any differences between Jesus's commandments and God's commandments? I always read about Jesus's commandments as something new in the bible; those commandments changed the way Christians see the Moshe writings. 

The bible  commentaries in this page of Rev 14:12 don't explain about the commandments of God, where saints keep them and have the faith of Jesus, nothing about  Jesus's commandments. So, there are any difference or are the same?
Doubting Thomas said it well in his comment: "Jesus was just elaborating on God's Commandments from the OT; revealing their true meaning.". In that spirit, here's my elaboration.

In Matthew 5:21-48, there are six it has been said statements:


Do not murder
Do not commit adultery
Anyone who divorces his wife must give her a certificate of divorce
Do not break your oath
Eye for eye, and tooth for tooth
Love your neighbor and hate your enemy


In each case, Jesus says a little word, "but", and then goes one huge step further. Just to take the last one as an example:


  You have heard that it was said, ‘Love your neighbor and hate your enemy.’ But I tell you: Love your enemies and pray for those who persecute you, that you may be sons of your Father in heaven. He causes his sun to rise on the evil and the good, and sends rain on the righteous and the unrighteous. If you love those who love you, what reward will you get? Are not even the tax collectors doing that? And if you greet only your brothers, what are you doing more than others? Do not even pagans do that? Be perfect, therefore, as your heavenly Father is perfect.


See the above verses or the full chapter for more.

Finally, note that Jesus Himself saw no difference. As He mentions just before the above verses:


  Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. I tell you the truth, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished.


Matthew 5:17-18