Relationship between Sunnah and Hadith

The usual source of information about the Sunnah is the report from the Hadith.
Generally speaking, A Hadith could be on any topic referring to moral conduct, current event, historical event, future event, the next world, legal rulings and other topics.
A Sunnah however should be related to moral conduct or behavior of some sort. For example, the following Hadith provide us with a Sunnah.
         “It was related by Anas that the Prophet will pass children and wish them peace” (Bukhari and Muslim).
              It is therefore Sunnah when passin g children to greet them. In another example, it was reported by Muhawiyya Ibn Al hakam.
“By my father and mother I never saw a teacher either before or after him who taught better than Prophet”
“By Allah he never look severe or exusted or revited (AbuDahud, Muslim and Nisa’i)
It is therefore Sunnah for a Teacher to avoid severity and harsheness towards his teachers.
However the following Hadith those not any Sunnah “It was related by Abu Huraira that the Prophet (S.A.W) said the best of you in the day of ignorance

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