In a general Wi-Fi network, there are really only 2 ways of networking systems. The first is the AP, or Access Point. The second is the wireless adapter. Both are available in various forms.

Access Point

The essential Access Point is a system that connects a wired network to a wireless one, broadcasting a signal out to client devices. Basically, it is a network switch with a wireless card connected.
Access Point: Router

A router is an Access Point with Network Address Translator capacity. It is used to translate data from 1 network to another, generally from a private network out to the wider Internet.
Access Point: Bridge

A bridge is access point that receives a signal from a different access point and forwards it over a wired network. These are used when the cost of running a wire among 2 parts of a building is prohibitive.
Wireless Adapter

A wireless adapter is a system that connects in PC, giving it the capability to receive and broadcast wireless networking signals.
Wireless Adapter: USB & PC Card

A USB wireless adapter plugs in PC via a USB port. With higher speed wireless networks, USB can make a bandwidth bottleneck, restricting speeds. Their benefit is that they are less expensive and far easier to install. PC card adapters are similar, but usually have higher overall speed.
Wireless Adapter: PCI

These are greater to USB adapters because they connect to a computer's motherboard directly, with much higher speeds. They are generally found in laptops with integrated wireless and on desktop computer.