What are the individual functions that make up the device?
The ADSL modem: An ADSL modem is much like a conventional dial-up modem in that it translates digital information into analogue waveforms that can be transported between computers over a telephone line. ADSL modems use a different modulation technology that allows much higher data rates than regular modems as well as the possibility of sharing a phone line with a conventional telephone service. Consequently, an ADSL modem can be permanently connected to the Internet without interfering with either incoming or outbound telephone calls. The only catch is that an ADSL line filter should be attached to any telephones using the same line as the modem.
The term ADSL router is a bit of a misnomer in that a router doesn't particularly care whether it is connected to an ADSL service or some other network connection. All a router does is 'route' data packets between two networks. On one side you have your local area network (LAN), and on the other side there is the Internet - whether it is connected to the Internet via ADSL, cable or any other method. Subsequently, an ADSL router is a device designed for use with ADSL services, which more often than not means it incorporates an ADSL modem. Because of this confusion in the terminology, it is worth checking whether an ADSL router has an integrated modem or not before you buy it.
The switch: A network infrastructure component to which multiple nodes attach. Unlike hubs, switches typically have internal bandwidth that is a multiple of link bandwidth, and the ability to rapidly switch node connections from one to another. A typical switch can accommodate several simultaneous full link bandwidth transmissions between different pairs of nodes.
The wireless access point:
The wireless access point is designed to provide access to local area wireless devices, commonly 802.11a, 802.11b, 802.11g or 802.11n. It is not designed for connecting to wireless Internet, as that requires a special kind of modem.