In order to distinguish between sunnah and hadith, we (I mean the school of thought I am representing) tend to highlight a few features:
i) Sunnah is always an act of the prophet, alaihissalaam, while a hadith is a report of his statement, act, silent approval or an incident that took place in his life.
ii) Sunnah has come down to us from generation to generation while hadith has been reported, in most cases, by one individual to another. Thus the act that qualifies as sunnah is undoubtedly authentic — quite as authentic as the Quran itself — while hadith, at best, carries a strong probability that it may have been correctively reported. This is because God Almighty arranged the two sources to be the way they are: He arranged sunnah to remain completed beyond doubt, because it was to be a part of His last message and allowed hadith to be a human effort at preserving information about the prophet.
iii) Sunnah is clear in what it stands for where as the context of a hadith had to be understood (and therefore interpreted) by all the narrators involved in the chain of transmission. The process of interpretation has also got to be done now by whoever is to benefit from a hadith.
iv) Sunnah has to be religious because the prophet, alaihissalaam, like all other prophets, came to give God’s message in the form of religion to mankind.
The last point of differentiation is quite clear, but has been made to appear not quite as such by the people who have attempted to present Islam as a way of life. The question is that if it was a way of life in which everything — including the minute details of practical life — had to be taken from the prophet’s life, then it should have been the prophet himself who should have told people to do so. When he clarifies that he had come only to deliver what is religion from God, who else has the authority to alter that understanding?
As for the question as to how can we distinguish a sunnah from a non-sunnah in the literature of hadith, we’ll have to look for practices that are mentioned in hadith which are also being universally followed amongst Muslims as such. Prayers, Jumu’ah prayers, funeral prayers, bathing of the dead and many other practices are the ones that are mentioned in hadith and Muslims have adopted them in their lives as a part of their religion.
Interestingly, this test of universality is the best guide in knowing the antithesis of sunnah — bid’ah — as well. If there is a practice that has gotten introduced in the name of religion in a certain region but is on confined to a certain region alone, it is a bid’ah, like the rituals performed in the subcontinent after the death of a dear one.
We know that the prophet, alaihissalaam, travelled on the backs of camels, horses, and donkeys; he advised people to resort to the medicines that were available during his times; he had his own taste for dishes which were different from the tastes of others; and he fought battles with swords and other forms of equipment of warfare that were available during his times. Muslim scholars have never considered any of these acts of him as sunnah, because they have nothing to do with religion.
I agree that at times there can be a difference of opinion on certain acts of his whether they were religious or not. This difference of opinion occurred during the time of the prophet as well. In such cases, it seems that the following criterion would help. Any act that belongs to any of these categories is religious, otherwise it is not:
i) Worship, remembrance of God etc.
ii) Physical cleanliness
iii) Cleanliness of edibles
iv) Ethics and morality.
I hope I have clarified my point.