The Quran:
Is the book or the words of Allah, it is a divine text.
Tafseer:
Refers to any kind of human interpretation of the Quranic text. It might be based on other Quranic verses, Ahadith, historical events. linguistic views or other sources. It might also be a book extracting rulings from the Quran etc.. So it is similar to exegesis as far as I know.
Hadith, ahadith and sunnah:
- Hadith is the singular of ahadith or sometimes written Hadiths it includes all transmitted sayings or doings of the Prophet. Note that many hadith collections also include sayings and doings of the sahaba (the companions of the Prophet Muhammad) and tabi'yn (those who met the sahaba): In summary one could say those people of the 1st maybe 2nd Hijri century. But strictly speaking a hadith refers only to what Muhammad () did or said beyond Quran. Anything else is better known among scholars as athar (trace) or khabar (news).
- Hadith also includes what is called hadith Qudsi: This is a divine word which Muhammad said in his own words or something he reported about Allah.
- Sunnah (in Arabic sunnah means path, so anything which is done the way Muhammad did is part of the sunnah) to some extent (as Hadith also include some historical evidences) includes all of this so if you hear people saying "this is sunnah" this means this is something the Prophet did or recommended or asked people to do. Hadith rely a lot on sane narrator chains as they mostly were compiled in the 2nd Hijri century. Those chains are examined in what is called ilm-ar-Rijal a part of the hadith sciences. Hadiths can only be considered as sane (sahih) when they don't disagree with the Quran and have enough evidences for sane narrator chains...
There are also commentaries on Hadith collections explaining the meaning or showing the rulings in ahadith or showing grades of sanity or weaknesses in the hadith. Mostly we call a commentary or interpretation of a Hadith "sharh".
Note that shi'a also consider sayings or fatwas of their Imam's as sunnah AFAIK. So my answer covers the primarily the sunni view and might lack details on the shi'a view.
There are also other books like biographies of the Prophet which mostly start by quoting the situation in the Arabic peninsula before the birth of Muhammad, also quoting Abraham, his son Ismael and how Muhammad is a descendant of him, the tribes of Mekka (and Medina as the family of Amina the mother of Muhammad lived in Medina or Yatrib) and their relation ... These books are called seerah or sira or in plural syar books. Mostly they are reports based also on narrator chains, but most of them have certain issues if one starts examining them from a hadith science view! These books may not have a major impact on the theology or rulings, but may explain how and why some rulings have come up and give a background for the jurisprudence.
So far this is related to Muhammad or what he has transmitted to us from our Creator.
Later scholars started to use Quran and sunnah to define rulings this was the birth of madhabs or schools of jurisprudence. And many Muslims only know Islam based on the rules of one of these schools. And if we start quoting those books that would be a very long list. Note that most schools of jurisprudence (fiqh) or at least those who survived until this day have defined the sources they rely on in a science called osol-al-Fiqh.
