Routers and switches are networking devices that connect computers and networks, but they operate at different layers and have different functions. Routers operate at the network layer (layer 3) and use IP addresses to direct traffic between networks, while switches operate at the data link layer (layer 2) and use MAC addresses to direct traffic within a local area network. Some key differences are that routers can perform tasks like network address translation, have fewer ports, and take longer for routing decisions than switches.