A pause, please. Bow your head in memory of the word "advanced." Third Edition no longer goes by the name Advanced Dungeons and Dragons.
The original Dungeons & Dragons and first edition AD&D were separate games. Dungeons & Dragons was a series of boxed sets with softback, thin rulebooks. Advanced Dungeons & Dragons began the hardcover-with-tiny-print tradition. AD&D's rules were (and are in D&D Third Edition) rather more complex.
A simple example would be alignment. Dungeons & Dragons characters could only have three alignments: lawful, neutral, and chaotic. With apologies to the anarchists among us, classic Dungeons and Dragons equated order with good and chaos with evil. In AD&D/Third Edition, alignment is on two separate axes: lawful to chaotic and good to evil.
Since the demise of the original boxed sets, Wizards of the Coast decided that continuing to call the game "Advanced" Dungeons & Dragons made no sense and risked scaring off prospective players. So now we have, simply, Dungeons & Dragons. It's all one system; even the new introductory boxed set uses a selection of the same rules.