Many Muslims often mix up when the term Sunnah arises in discussions. This word has three separate meanings.
The first sense of Sunnah is in the setting of shari’ah rulings, in which Sunnah is like with the mandub or “recommended”, meaning something that one deserves a reward in the next life for doing; such as using the miswak to clean one’s teeth before prayer, but is not punished for not doing. It can been contrasted in this context with the “wajib” or obligatory, meaning something that one is rewarded in the next life for doing, such as performing the prescribed prayers – and deserves punishment in the next life for not doing. The Sunnah in this sense is at the second level of things Allah has asked of us, after the wajib or obligatory.
The second sense of Sunnah is in the setting of identifying textual sources, as when the Qur’an is contrasted with the Sunnah, meaning the hadith. In this sense, Sunnah is strictly synonymous with hadith, and is used to distinguish one’s evidence from that of the Qur’an. One should note that this is quite a different sense from the above-mentioned meaning of the word Sunnah, though sometimes people confuse the two, believing that the Qur’an determines the obligatory, while the hadith determines what is merely Sunnah or recommended, but in fact, rulings of both types are found in the Qur’an, just as they are in the hadith.
The third sense of Sunnah is the way of the Prophet (s.a.w), embodied in the things he said, did, and in his noble states of heart; together with the things he approved of in others (whether by clear confirmation, or by allowing them to be done in his presence without condemning them), and the things that he intended to do but did not get the chance, such as fasting on the ninth of Muharram (Taasua). Here, Sunnah simply means the Prophets way (s.a.w), and is not to be confused with either of the two senses mentioned above. In contrast to the first sense, his Sunnah or way (s.a.w) includes not just the recommended, but rather the whole shari’ah, the entire spectrum of its rulings, whether obligatory (wajib), recommended (Sunnah), permissible (mubah), or avoiding the offensive (makruh) or unlawful (haram). And in contrast with the second sense, his Sunnah or way (s.a.w) is preserved not only in the hadith, but first and foremost in the Qur’an, for as Aisha (r.a) noted in the hadith of al-Bukhari, “His character was the Qur’an”.
The confusion and non sequiturs that often result when Muslims discuss the Sunnah could perhaps be better avoided if these distinctions were kept in mind.
The confusion is quite dominant. As you've put it, some elements within the sunnah are themselves obligatory. We should also not forget the command of Allah in the Quran that ''whatever he has ordained you to do do it and whatever he has fordidden you to do shun it.''
Indeed these two words are very confusing.In my view, sunna has something to do with actions,conduct, behavier including methods of doing things,where as hadeeth is something to do with explanation of the above.I can therefore say that sunna is practical thing while hadeeth is theory.