Routers – connects devices together and transmits layer 3 packets between them (routing).

Routers are networking devices that connect the parts of the TCP/IP network together for the purpose of routing (forwarding) IP packets to the correct destination. Routers do the equivalent of the work done by each post office site: They receive IP packets on various physical interfaces, make decisions based on the IP address included with the packet, and then physically forward the packet out to some other network interface. Routers operaterate Layer 3.

Routing protocols helps router to build and maintain the routing table in routers.
Example of routing protocols are RIP, RIPv2, EIGRP,OSPF etc.

The Routed protocols are responsible for flow of data packets from one network to another network. Routed protocols sends the data packets to correct exit interface of the router. Routed protocols configured on interfaces of the router. Example of routed protocols are IP, Ipv6, IPX and Appletalk.
Routed protocols are basically addressing schema of the interfaces of router. Router identify the destination network of a data packet and send the data packet to correct exit interface. The concept of subnetting takes place in routed protocols.