What is the difference between Fullmetal Alchemist and Fullmetal Alchemist: Brotherhood?

I have read on Wikipedia that:

Fullmetal Alchemist: Brotherhood is the second anime television series based on Fullmetal Alchemist, the first being 2003's Fullmetal Alchemist, and unlike its predecessor it directly follows the events of the manga.

Fullmetal Alchemist and Fullmetal Alchemist: Brotherhood are they telling the same story or they are different?