You're referring to the four Gospels, which are also the first four books of the New Testament. They are Matthew, Mark, Luke, and John.
Each Gospel gives a unique description of the same event based upon the writer's perspective. Matthew and John (two of Jesus' original disciples) give us Gospels that are based on eyewitness accounts.
They observed what Jesus said and did and recorded those things. The Bible does not tell us if Mark and Luke were followers of Jesus during His lifetime. We do know that they were closely associated with the Apostle Paul and ministered with him.
Their Gospel accounts were most probably based on interviews with Jesus' original disciples and other eyewitnesses to His life. For example, Luke no doubt had a very detailed discussion with Jesus' mother Mary as he gives a very moving and detailed description of Jesus' miraculous conception and birth.
Each of the Gospel writers might describe differently what they saw or heard, but all of them would be correct. If we took what they all said and put it together, we'd come up with a more complete picture. This is how we should view events that are described in more than one of the Gospels.
It is also helpful to recall the role of the Holy Spirit in the writing of the Gospels. Here's a Scripture that explains this vital role:
But the Counselor, the Holy Spirit, whom the Father will send in my name, will teach you all things and will remind you of everything I have said to you.The Holy Spirit helped the authors of the four Gospels by bringing events back to their remembrance the way they first observed them and providing reliable eyewitnesses to the life of Jesus.
(John 14:26 NIV)
The Gospels are God-inspired, yet written from the individual's point of view. In my personal study of the Bible, I find the different analysis of the same event to be very helpful when desiring the entire sequence of biblical events.
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