How does a router differ from such devices as repeaters, bridges, and switches?

Please see below as the answer is self-explanatory

Explanation:

Repeaters, bridges and switches, route packets only within the limits of  their own physical networks, using the physical hardware addresses of the different devices connected to the network.

On the contrary, routers are devices that interconnect physical networks, with one physical interface per each network to which the router is connected to.

Routers use logical addresses -called IP addresses in the TCP/IP suite, which operate at the network level, and take charge of the delivery of packets beyond the network that originated it, based on the IP address of the destination host.

Only when the IP destination address is within the same physical network as the router, it transforms the IP datagram in a Frame and sends it using the physical hardware address of the host.

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