Future Trunks:
Trunks is the son of Bulma and Vegeta. At the start of the Android saga, 3 years before Chibi Trunks is born, Future Trunks goes back 20 years in time from his dimension to warn the Z warriors about some androids who would kill them. In his time the androids #17 and #18 had killed all of the Z warriors and only Trunks and his mother survived. He had never seen his father before so he also wanted to come back in time to meet him. When he first lands on Earth, he kills Freeza and King Cold, who have also arrived there. The Z warriors are shocked that there is someone else they didn't know about who was a Super Saiyan. Future Trunks then tells them that the androids would come in 3 years time and they must train until then. When 3 years have passed, Future Trunks comes back to the present timeline to help fight the androids and Cell.

Chibi Trunks:
Chibi Trunks (aka the 'present time' Trunks) is born in the Android saga, 3 years after Future Trunks first traveled to the present timeline. His best friend Goten is born a year after him, after the Cell game is over. They were both stronger than their parents at their age and were able to turn Super Saiyan very young too. In the Buu saga, when Trunks is 8 and Goten 7, Goku (who has been dead for the past 7 years) is granted a day on Earth for the Tenkaichi Budokai and teaches Trunks and Goten the fusion dance so they can fuse into Gotenks to try and defeat Buu. Trunks' sister Bra is born at the end of DBZ and is 13 years younger than him.
Trunks is a main character in DBGT, when he also becomes president of his family's Capsule Corp company. He goes around the universe with kid Goku and Pan to look for the Black Star Dragon Balls.