Outbox and Sent are both terms used in e-mail systems like Gmail. Both refers to where your composed messages or emails are stored. However, both Outbox and Sent are not totally the same. Outbox is like a temporary box holding all messages or emails to be sent out. When you compose a message, and you send it, it first moves to the outbox waiting for the recipient to connect to the internet and then receive the mail. All the mails that do not get to the recipient are stored in the outbox.
Sent, on the other hand, refers to a folder where all the messages that are successfully delivered are stored. So, immediately, the mail gets to the recipient; it moves straight into the sent folder. Outbox messages can still be reviewed to know if there are changes you would like to make; they can be re-edited. Outbox messages can also be deleted; in case you no longer want it to be sent. However, once it moves into the sent folder, it means the message has been received by the recipient, and as such, it can no longer be re-edited.