Categories of Computers:
Mainframe
A mainframe computer is a high performance computer used for large-scale computing purposes that require greater availability and security than a regular computer can offer.
Server
A server is a computer designed to process requests and deliver data to other computers over a local network or the Internet.
Desktop Computer
A desktop computer is a personal computer that is designed to fit conveniently on top of a home or office desk. They are capable of running a wide variety of applications, but they are typically not super computers.
Workstation Computers
Workstation Computers are intended for use by one person, but have a much faster processor and more memory than an ordinary desktop computer.
Laptops
A laptop, also referred to as a notebook computer, is a personal computer designed for portability. This is the same laptop I have. :)
Portable Devices
Portable devices have a variety of purposes. They generally use proprietary operating systems. Many portable devices are even capable of connecting to wireless networks via wi-fi.