Look, it's not hard to understand. It's an easy concept. What I am saying now is pretty much the truth more or less.
*Major Spoiler alert*
In the beginning of DBGT, Goku got turned into a kid by Emperor Pilaf. He goes throughout almost the entire series as a kid, except for when he goes SSJ4, and the last episode, which I will explain in a moment. The second to last episode or so of DBGT, after El Shenron (soon to be Sin Shenron when DBGT comes out in the states) was destroyed by Goku's spirit bomb, the Dragon appeared without being summoned, and said that he was not going to grant any more wishes because of all the trouble that came about. He asks that Goku takes a ride on his back. Well, Goku just ends up vanishing off the face of the Earth, probably I believe going back to Heaven again.
Now we fast forwards 100 years. We have Goku Jr. and Vegeta Jr. who are decendants of Goku and Vegeta respectively (Goku Jr. probably Pan's grandson, and Vegeta Jr. being Bra's grandson). Goku Jr. and Vegeta Jr. are not the Son Goku and Vegeta we know from the rest of Dragonball Z and Dragonball GT. They are different people. Pan ends up seeing what she thinks is an adult Son Goku (the stupid, powerful, and sloppy eating Goku from DB/Z/GT) in the crowd. She chases after him, and he ends up disappearing. He probably was allowed to go watch the fight by the Elder Kai or something. But that pretty much was the end of the series. So we have Goku, Vegeta, Goku Jr., and Vegeta Jr. They are all different people.