Qur'an is Allah's word. Hadith is the word of Allah's Rasul, Sayyidina Muhammad, Sallallahu Alaihi wa Sallam.
One from Heaven and the other from right here, Earth. But the isomorphism -- how the two match and correlate together -- between the two is beyond what a human mind can imagine.
Here is one example.
Allah says in the Qur'an:
Wa Tawakkal Alal Hayyil-Ladhee Laa Yamootu.
"And put your trust in the Ever-Living God who does not die."
Muhammad, Sallallahu Alaihi wa Sallam, says in the Hadith:
Tawakkaltu Alal Hayyil-Ladhee Laa Ymootu.
"I have put my trust in the Ever-Living God who does not die."
People! If this is not a miracle, what is? And if this does not make you a Muslim, what will?