A router is the smartest, and most complicated of the bunch.
Routers come in all shapes and sizes,from the small four-port
broadband routers that are very popular right now,to large
industrial strength devices that drive the internet itself.
A simple way to think of a router is as a computer that can
be programmed to understand, possibly manipulate, and route
the data its being asked to handle. For example, broadband
routers include the ability to "hide" computers behind a type
of firewall, which involves slightly modifying the packets of
network traffic as they traverse the device.All routers include
some kind of user interface for configuring how the router will
treat traffic. The really large routers include the equivalent
of a full-blown programming language to describe how they
should operate, as well as the ability to communicate with
other routers to describe or determine the best way to get
network traffic from point A to point B.
A PROXY
A FIREWALL
a proxy is a central machine (P) in a small network that
allows other machines (A, B and C) in that network to use
a shared Internet connection. The software on the central
machine is called proxy software. The proxy is also
called 'server' or 'gateway'. Most proxy software works
perfectly for browsing the Web, sending files with FTP
and sending E-mail. Normally proxy software does not
understand IRC connections or DCC File transfers by default.
Very often this is easily fixed!
Lots of companies use proxies to allow multiple machines
access to the Web.There are a lot of proxies that you can
use yourself in a small network to give all your computers
access to the Net through one modem, cable of (A)DSL line.
Examples of proxies are the Internet Connection Sharing
(ICS -built in in Windows), and programs like
Winproxy and Wingate.
A firewall is not that different from a proxy.
A firewall again offers Internet access to lots of
other computers on a network but is mostly deployed to
provide safety or security; control over the information
going in and out the network.Firewalls are used in business
environments, at schools, universities and the like.
Please keep in mind that most proxies and firewalls
in use in business situations are there for a reason;
to protect your work environment from the evil Internet.