In Islam, the Arabic word sunnah has come to denote the way Prophet Muhammad (saas), the Messenger of Allah, lived his life. The Sunnah is the second source of Islamic jurisprudence, the first being the Qur'an. Both sources are indispensable; one cannot practice Islam without consulting both of them. The Arabic word hadith (pl. ahadith) is very similar to Sunnah, but not identical. A hadith is a narration about the life of the Prophet (saas) or what he approved - as opposed to his life itself, which is the Sunnah as already mentioned.For example, it is in the Hadith that you see the requirement to execute apostates (those who renounce Islam):
Narrated 'Ikrima:and regarding Jihad
Some Zanadiqa (atheists) were brought to 'Ali and he burnt them. The news of this event, reached Ibn 'Abbas who said, "If I had been in his place, I would not have burnt them, as Allah's Apostle forbade it, saying, 'Do not punish anybody with Allah's punishment (fire).' I would have killed them according to the statement of Allah's Apostle, 'Whoever changed his Islamic religion, then kill him.'"
Allah's Apostle said, "The Hour will not be established until you fight with the Jews, and the stone behind which a Jew will be hiding will say. "O Muslim! There is a Jew hiding behind me, so kill him."
Allah 's Apostle said, " I have been ordered to fight with the people till they say, 'None has the right to be worshipped but Allah,' and whoever says, 'None has the right to be worshipped but Allah,' his life and property will be saved by me except for Islamic law, and his accounts will be with Allah, (either to punish him or to forgive him.)"