Facebook chat and messenger have many things in common. They are both associated with Facebook and you have to have an account with Facebook in order to use either one of them. However, Facebook chat was first created by Facebook in 2008. Then it was updated in 2010 and changed in 2011 to become Facebook messenger. In messenger and chat, you can message a friend with a message without anyone else knowing.
Messenger has more features than Facebook chat. Chat was created first and then Facebook had a better idea to make this chatting system better. That is when Messenger was created and many users enjoyed having more features to use when chatting with someone. Maybe in the future there will be even more features on Messenger.