In [1], a router is designed to route data packets from one interface to another. A firewall inspects the data packets and adds filtering and blocking of data packets with services like NAT
Think of a traffic cop at an intersection. He will carefully and decisively direct the traffic the direction it needs to go, this is a router.
You have another cop that has a gun. He does not care where the traffic is going, he just wants to know what the traffic is doing. If it is "bad" then he will shoot that "blocked" traffic onsite and toss it in the bit bucket. This would be a firewall.
Now take the traffic cop and give him the gun. He will now direct traffic as well as make sure it is "good". He is now a router/firewall.
