According to Purpose
General purpose Computers
Special Computers
General purpose Computers
A ‘General Purpose Computer’ is a machine that is capable of carrying out some general data processing under program control.
Refers to computers that follow instructions, thus virtually all computers from micro to mainframe are general purpose. Even computers in toys, games and single-function devices follow instructions in their built-in program.
Special purpose Computers
A computer that is designed to operate on a restricted class of problems.
Use special purpose computer equipment to obtain patient diagnostic information.
Source:
http://www.wisegeek.com/what-is-a-digital-computer.htm