To clarify a leetle bit more (why not?) Dragon Ball and Dragon Ball Z together are animated adaptations of the manga Dragon Ball. It's all one manga, one story. It starts out with Goku at 12 years old as a very dirty humor martial arts story. About a third of the way through, a little bit after Goku and his friends reached adulthood and the emphasis turned more from comedy to action, the TV series renamed itself Dragon Ball Z and continued adapting the manga otherwise uninterrupted. Dragon Ball GT was a separate TV series continuing after the Dragon Ball manga ended.