Initially many companies created more than one website, each of which was suitable for a different receiving device. Now there are so many different devices and sizes , creating different sites is no longer practical and probably near to impossible.
Responsive Web Design
Responsive Web Design (the term was coined by Ethan Marcotte in an article for A List Apart) allows you to create web pages that respond to the environment/device in which they are viewed.
This is achieved by creating Media Queries that are part of your CSS.