Thank you for the Biblical question, “What is the differentiate the distinction between the letter and the gospel?”
The similarity between the Epistles (Letters) and the Gospel is that both of them were written to a certain people group. The Gospel does not state to whom it is written while the Epistles generally has an addressee state to it as the church of God in Corinth (I Cor. 1:2).
The difference between the Epistles and the Gospel is the content. The Gospels are about the words and works of Jesus on earth, while the Epistles are about words and works to the followers of Jesus. The Gospels are about The Son of God, while the Epistles are about the children of God. The Gospels are about Jesus in the world, while the Epistles are about Jesus in the believers. The Gospels are about the proclamation of the Good News to Israel, while the Epistles are about the proclamation of the Good News to the world.
SUMMARY: The Gospels are about Jesus while the Epistles are about the Children of God.
For more perspectives:
https://www.quora.com/What-is-the-differentiate-the-distinction-between-the-letter-and-the-gospel