The question of hadith (Arabic: حديث pl. أحاديث, "words and deeds of Muhammad") falling within the abode of the sunnah is a disputed one, and is highly dependent on the context. In the context of Islamic Law, Imam Malik and the Hanafi scholars assumed to have differentiated between the sunnah and the hadith. In some instances, for example, Imam Malik is supposed to have rejected hadiths that reached him because, according to him, they were against the 'established practice of the people of Medinah'. According to other opinions, sunnah constitutes of what Muhammad believed, implied or tacitly approved and was noted down by his companions in form of what is today known as hadith. In Shi'a Islam, the word 'Sunnah' means the deeds, sayings and approvals of Muhammad and the twelve Imams who Shi'a Muslims believe were chosen by Muhammad to lead the Ummah - the world muslim community.
In the context of biographical records of Muhammad, sunnah indeed often stands synonymous to hadith as most of the personality traits of Muhammad are known through descriptions about him, his sayings and his actions, after becoming a prophet at the age of forty.
Through research on the transmitters of Hadith (isnad), scholars of the science of Hadith came up with the system of knowing the different categories of Hadith, and how to evaluate the text (matn) in order to establish if the text is correct, good, weak, or false. There is a tradition both of historical biography (Ilm ar-Rijal) of Muhammad and of validating hadith — isnad or “backing”.
Sunnah, on the other hand, is established through the practical examples and not via these texts in Islamic law, but mostly through the hadith texts as far as prophetic biography, traits and examples are concerned. For example, prayers, both individual and congregatory, were taught by Muhammad to his followers by practical example and since then have been transmitted generation-to-generation through practical learning. Their documentation in form of Hadith only happened later, but their actual learning and transmission has always been through practical means. On the other hand, many traits about Muhammad, such as his style, his habits, and his dealings with others, is known primarily through hadith.
Traditional Muslims however, believe that verses such as "So they routed them by Allah's leave and David slew Goliath; and Allah gave him the kingdom and wisdom, and taught him of that which he willeth. And if Allah had not repelled some men by others the earth would have been corrupted. But Allah is a Lord of Kindness to (His) creatures." (2:151) justify the Sunnah. Many of these sunnah had their roots coming from Abraham as it is mentioned in Quran, "Who is better in religion than he who surrendereth his purpose to Allah while doing good (to men) and followeth the tradition of Abraham, the upright? Allah (Himself) chose Abraham for friend" (4:125).
Had Muhammad's only role been to deliver the verses, the remaining parts of the verse: "purifying you, and teaching you the Book and the Wisdom..." would not have been there. The traditional view holds that the above verses imply that Muhammad's mission is to deliver the message as well as teaching the explanation of the Book (the Quran) and the Wisdom behind it to the people; it is not just to relate the verses of the Quran and leave.
In addition, the verse: "Verily in the messenger of Allah ye have a good example for him who looketh unto Allah and the Last Day, and remembereth Allah much." (33:21), further emphasizes that Muhammad's example is divinely inspired and to be followed by Muslims.
According to traditional Muslims, the point being emphasized in the verses quoted by the Quran alone argument is that Muhammad is not to be worshipped or deified and that his role is to deliver the Quran,with comprehensive explanation and guidelines on how to live in the Quran—guidelines which have been preserved in Sunnah.
Musa, Aisha Y. Hadith as Scripture: Discussions on the Authority of Prophetic Traditions in Islam, New York: Palgrave, 2008. ISBN 0230605354.