This is an amazing question, and hopefully I can provide an answer that will clear your confusion.
What is the Sunnah?
Sunnah is what the Prophet (SAW) did on regular basis, said, or approved (approved an action that was done by the companions, whether he approved it verbally or did not object it). I will provide an example for each one.
- a Sunnah that he (SAW) said: is basically any authentic Hadith that was narrated by the companions.
- a Sunnah that he (SAW) did on regular basis: like Witr prayer or the 2 Rak'at before Fajr prayer, etc....
- a Sunnah that he (SAW) approved: when the companions were eating a Lizard (those spiny-tails lizards) on the same table with the Prophet (SAW), he (SAW) did not eat from it, but at the same time he (SAW) did not stop them from eating it.
What are the Ahadith?
Ahadith are very similar to Sunnah; any narration of the 3 Sunnahs mentioned above is called a Hadith. Moreover, any incident that happened to the Prophet (SAW), even if it happened once, and was narrated by one of the companions is called a Hadith, like the Hadith of the journey of Ta'if or the Hadith of the night journey (Al-Mi'raj), we don't say the sunnah of Al-M'iraj or the sunnah of Ta'if.
How they differ? How they are similar?
Now, you could easily spot the similarity between Hadith and Sunnah from what I mentioned above; any authentic narration for any Sunnah of the Prophet (SAW) is a Hadith.
The difference is basically, from my own understanding, the context in which you use either one. I will give you some examples:
- How the Prophet (SAW) lived his life; how he used to eat, how he used to sleep, etc, is called Sunnah, we don't say this the Hadith of the Prophet, but we say this is the Sunnah (way of life) of the Prophet (SAW). However, and as I mentioned above, if that incident happened only once in the life of the Prophet (SAW), we say there is a Hadith from the Prophet (SAW) about this incident, we don't use the word Sunnah here.
- Following the rules of Sharia and not exaggerating or innovating anything new in the religion is called Sunnah, not Hadith.
- When talking about narrations, we use the word Hadith, not Sunnah. We say this Hadith is authentic and this one is weak, we don't say this Sunnah is weak.
Are there any firm references to the Sunnah? The Ahadith are
entrenched in a dozen or so fixed sources (not going into Sunni vs
Shiaa differences here). Are there any firm books that act to be
references for the Sunnah?
I highly recommend a book called زاد المعاد في هدي خير العباد (Zad Al-Ma'ad) by Ibn Al-Qayyim as a very good reference for the Sunnah.
Please forgive me if I failed to answer your questions.
Indeed Allah knows best!