Mirai no Trunks "Future Trunks"- The Daizenshyu lists both Future and Little Trunks as the same character, but since they're so different, I'm dividing them into two seperate sections. Future Trunks comes to the present from the year 784 AD. His future is a bleak one. Son Gokou died from a viral heart disease he picked up on the planet Yardrat and soon three years later, the Atificial Humans showed up, and killed all of the Z Soldiers, except Gohan. As Trunks grows older, Gohan trains him, but eventually he is killed by the Artificial Humans. (In the anime, it was Gohan's death that made Trunks angry enough to turn SSJ, in the manga, he was was able to turn SSJ prior to Gohan's death). His mother, Buruma, invents a Time Machine which will allow him to travel back through time to the year 764 AD and give Gokou the medicine to cure his disease. (The medicine had not been invented till many years after Gokou's death). He also came to warn Gokou of the arrival of the Artificial Humans three years from then. With this accomplished, he returns to his future, and waits 6 months for the Time Machine to recharge. (It can only be assumed that he trained during this period of time). When the Time Machine is fully recharged, he returns to the same time he was in before, but three years later. From this point he sticks around, and his identity is slowly revealed to everyone. In other words, the fact that he's Vegita and Buruma's son. During the Cell Game, Trunks is killed, which causes Vegita to FLIP (proving that he actually does care for his son) but he's quickly ressurected by the Dragon Balls. Soon after that he returns to his future in 785 AD. and is finally able to kill Androids 17 and 18, as well as the Cell in his time period three years later in 788 AD. Trunks then returns to the past again, (in the anime story-line ONLY), just to say "hi" to everyone and participate in a martial arts tournament, the events of which are shown in DBZ Movie 9. I don't normally go into this much detail, but I'd say Trunks is a pretty popular character, and this should answer most of your major questions about him. As a person, Trunks is fairly quiet. He doesn't say much except when he has something VERY important to say, or he's invited into a conversation. Trunks use a formal type of language. That's not to say he's uptight, he's just normally very polite. Even when fighting Cell, he keeps his cool and carries on a conversation with him. It's safe to safe that he's the type of person who would be willing to sacrafice himself so that others could live.
Chibi Trunks "Little Trunks"- I've been waiting to do this one, because I want to kill a myth which seems to be spreading. A lot of people say that Trunks is "spoiled and a complete brat". They say he's a complete contrast to Future Trunks, yadda yadda yadda. That's not true. Trunks is simply like any normal eight year old. Although Future Trunks is very polite and acts very different from an eight year old, (which would seem obvious since he's a young adult), Chibi Trunks can be seen developing into the same type of person that Future Trunks was during the end of DBZ, and through DBGT (If you count GT that is). However, there is a BIG difference between the two which no one ever seems to touch upon. Chibi Trunks is filled with pride much like his father. He has little faith in Son Gokou when he arrives, and doesn't believe that he's any stronger than his father. (Until he feels Gokou's ki when he turns SSJ3 of course). Trunks also defends his father valiantly when Buu attacks him, and is angered by the fact that someone like his dad could be beat up on so easily. Chibi Trunks is also very adventurous and is always looking to fight strong opponents. Another myth is that Goten is hesistant to embark on adventures with Trunks. Goten and Trunks both go nuts when they hear about Majin Buu and can't wait to see him, (and fight him). Trunks was born in the year 766 AD. and was eighteen years old when DBZ ended. Like Goten, he had the ability to turn Super Saiya-jin from an early age.
