[Computer Networking] What is the difference between a Router & a Adapter?

In Computer Networking, Router have the function of an Adapter, but a Router perform more duties than an Adapter.

Adapter enable a computer to "Adapt" to the current network setting set by the "Router", Router also adapts the network settings set by the modem or sometime by the computer.

Yet there is a crucial difference between an Adapter & Router. I can demonstrate the simple difference of adapters & routers in wireless networks. Most Laptops have Wireless Network Adapter, not routers, because it can only connect to one network point (A Wireless Network Router or another computer). But routers can connect to multiple computers or act as a network point for multiple devices, so the almost all the Internet-Sharing "box-thingie" we have in home is named Wireless Network "Router", not adapter.