I'm no scholar, and am myself relatively new to Islam, Alhamdulillah (praise be to God), so please take the following with a pinch of salt. My understanding is that the Quran is the word of God Himself. It is not an interpretation, it is not a translation, it is not divinely inspired and then written in the words of the Prophet (may God's peace, mercy and blessings be with him). It is not in the words of a human being - it is a verbatim copy of the words as God said them. The Quran contains no information about the context in which the words were revealed, it doesn't contain the dates or historical events or anything outside of the exact text revealed by God Himself. And that is why the Quran is also the ultimate miracle in Islam. It is the only revelation that is still with us in the exact form in which it was revealed.
Hadiths on the other hand are not the word of God. They are narrations passed down from person to person about things that the Prophet (peace be upon him) did or said. They are stories passed down from generation to generation by the noble Companions of the Prophet, till they were collected in text, and preserved along with the original chain of narrators. Hadiths are not necessarily well preserved, and in deed many may have been fabricated by those wishing to malign Islam. Many may have information lost (think of the game of Chinese whispers)... And so, a lot of emphasis is given on authenticating Hadiths, to make sure they are 'saheeh', or Authentic, before one follows them.
The reason why the 'rules' derived from the Hadith are so important is that the Quran tells us that the Prophet (peace be upon him) was sent to the whole world, as a Mercy, and as an example for us to follow. The Quran instructs us to do as the Prophet told us to do, and so the root of the authority of the Hadiths is the Quran.
I hope I was able to be of help, and if anyone sees a mistake, please correct me where I am wrong.