With a quit claim deed, one is essentially transferring whatever ownership they MIGHT have in a property to the second party.
So, in theory, John could go up to his neighbor Alex and say, "Alex, I think that you believe that you have an interest in that field that I own that is out back behind both of our properties. Why else would you keep parking your two quads and your two snowmobiles back there?" Alex the flatly denies that he has any interest in the field, but John doesn't believe him. Alex then offers to sign a Quit Claim Deed in regards to the field and promises not to park his vehicles there anymore. The two of them visit a real estate attorney and get the paperwork done up for $1,500. Alex has not transferred any ownership interest that he MIGHT have had in the land to John.
The only thing is that Alex really never DID own any part of the field. He doesn't have the ability to transfer full ownership to John or anyone else because he never had an ownership interest in the first place. He can still sign a Quit Claim Deed though. Any Joe off the street can renounce their non-existent interest in a piece of property with a Quit Claim.
A Warranty Deed, on the other hand, is a document which states that someone owns the property and has the right to sell it to another person. They "Warrant" (or guarantee) that no other liens have been placed on the property that are not being resolved at the closing table and they Warrant (or guarantee) that the new owner isn't going to get a call from Long Lost Uncle Joe ranting about how they were not allowed to buy the house in the first place because he owned 50% of it from years back.
The only proper way to Warrant (guarantee) that the title is free and clear and that the new owners will not have any title issues creating stress in their life is to to have a title company do a property title search for any hidden liens and then issue a title insurance policy that backs up the guarantee made by the sellers when they sign the Warranty Deed. This gives the new owners peace of mind knowing that IF an "Uncle Joe" does turn up, the Title Insurance Company will pay him off so he goes away and the new owners won't have to track down Uncle Joe's relatives that sold the property to them when those sellers have moved on to their new life in New Zealand.
I hope this little story illustration has helped clear up the issue for you.