From what I read, I understood that both the bastion host and the dual homed host are special computers that act as a link between the local network and the internet, so what is the difference between them?
Your question is a bit like asking what's the difference between a defense counsel and an attorney. An attorney is a person who has studied law and is licensed to practice it; defense counsel is the role an attorney can play in a specific trial.
"Dual-homed" describes the networking configuration of a host that has interfaces in two networks. "Bastion" describes the role it plays: provide safe, controlled external access to resources in one of those networks to authorized clients in the other.