Are the Mahdi and the Messiah one and the same person?
Yes. Messiah and Mahdi are titles, not two different people, and one person called by God can carry both. Because the Holy Qur’an shows that Jesus (as) has died, the promised one comes as an Imam from among the Muslims themselves.
The key to this question is that Messiah and Mahdi are titles. A title describes a task, not a body. Just as one person can be both a teacher and a father, one person called by God can be both the Messiah and the Mahdi. There is no contradiction in that.
Mahdi means “the rightly guided one”. It is not a rank a scholar can give himself. In history many have declared themselves the Mahdi, some even taking up arms, and none of them lasted. The true Mahdi is called by God, and God confirms him with signs that no human being could bring about.
A second question is decisive. Is Jesus of Nazareth still alive, or has he died? The verses above answer it. All the messengers before the Holy Prophet (saw) have passed away, and Jesus (as) himself speaks of God having caused him to die. Whoever has died does not return to this world. So the promised son of Mary must be someone else, someone who comes in the spirit and character of Jesus (as).
This is exactly what the hadith above says. The promised one will be an Imam from among the Muslims themselves. The word “descend” also does not mean that someone falls from the sky. The Holy Qur’an uses the same Arabic word for iron, for cattle and for the Holy Prophet (saw) himself. It describes something precious that God gives to people.
In this way the statements fit together. The Messiah whom Muslims await is born in their own community, and he is at the same time their rightly guided Imam.