The primary thought is Judas died by suicide by hanging himself: 
Matthew 27:3-5: (KJV) “Then Judas, which had betrayed him, when he saw that he was condemned, repented himself, and brought again the thirty pieces of silver to the chief priests and elders, saying, I have sinned in that I have betrayed the innocent blood. And they said, What is that to us? See thou to that. And he cast down the pieces of silver in the temple, and departed, and went and hanged himself.”

This plain statement clearly implies death by hanging.

Or, did Judas died by falling and his intestines bursting out of his abdomen? 
Acts 1:15-20: (NASB) At this time Peter stood up in the midst of the brethren…and said, Brethren, the Scripture had to be fulfilled, which the holy spirit foretold by the mouth of David concerning Judas, who became a guide to those who arrested Jesus. For he was counted among us and received his share in this ministry. (Now this man acquired a field with the price of his wickedness, and falling headlong, he burst open in the middle and all his intestines gushed out. And it became known to all who were living in Jerusalem; so that in their own language that field was called Hakeldama, that is, Field of Blood.) For it is written in the book of Psalms, Let his homestead be made desolate, and let no one dwell in it; and, Let another man take his office.” 

This sounds like while walking, Judas tripped, fell and ruptured his abdomen. Did he hang himself or he fall? Which is correct? BOTH are true. Both accounts are simply different aspects of Judas’ death. He died by hanging. His body stayed there, and eventually the rope or branch on which it hung broke, and his body fell headlong.

(Source: https://answersingenesis.org/contradictions-in-the-bible/how-did-judas-die/) “Gruesome as it is, Judas’ dead body hung in the hot sun of Jerusalem, and the bacteria inside his body would have been actively breaking down tissues and cells. A byproduct of bacterial metabolism is often gas. The pressure created by the gas forces fluid out of the cells and tissues and into the body cavities. The body becomes bloated as a result. In addition, tissue decomposition occurs compromising the integrity of the skin. Judas’ body was similar to an overinflated balloon, and as he hit the ground (due to the branch he hung on or the rope itself breaking) the skin easily broke and he burst open with his internal organs spilling out.” 

Why the difference in narratives? Matthew was reporting how Judas died. In Acts, Peter is establishing that what happened to Judas was a result of his suicide and horrific fall from the tree. It shows a sense of shame for the betrayal. This, along with fulfillment of scriptural prophecy, prompted them to officially replace the twelfth apostle. 

Peter quotes parts of the Psalms as evidence: 
Psalm 69:25-26: (NASB) “May their camp be desolate; may none dwell in their tents. 26For they have persecuted him whom You Yourself have smitten…”

Judas fulfilled that prophecy. He persecuted Jesus by turning him over to the authorities. 

Psalm 109:6-8: (NASB) “Appoint a wicked man over him, and let an accuser stand at his right hand. When he is judged, let him come forth guilty, and let his prayer become sin. Let his days be few; let another take his office.” 

Peter explained that Judas needed to be replaced, per prophecy.

Different Scriptures often reveal different parts of a story. It is important to observe how the harmony of various details actually fit together. Remember there is more to the story.

Additional Resources:
Christian Questions Podcast 
Bible Contradictions Series