Routers are physical devices that join multiple wired or wireless networks together. A wired or wireless router is connects networks, and that the router operates at the network layer of the OSI model.
A router is a device that forwards data packets along networks. A router is connected to at least two networks, commonly two LANs or WANs or a LAN and its ISP’s network. Routers are located at gateways, the places where two or more networks connect.
Routers use headers and forwarding tables to determine the best path for forwarding the packets, and they use protocols such as ICMP to communicate with each other and configure the best route between any two hosts.
A network adapter is considered a hardware device that connects a PC to the network. Without such a device, connecting a PC to the network would be impossible. There are two types of network adapters: external and internal.
External adapters: External adapters simply sit near or some place close to the computer. Usually you plug the network adapter into the PC by way of a USB cable. These are considered the fastest and easiest way to set up your network, especially if it is your home network.
Internal adapters: Internal adapters are installed inside the computer in an expansion slot; more like a PCI slot, if one is available.
Network splitters are exactly what they sound like. They split connections. They are used to add on the network when cabling is slack.