Personal computer: A single-user computer based on a microprocessor.  

Purpose: It can be defined as a small, relatively inexpensive computer designed for an individual user.

Workstation: A powerful, single-user computer. A workstation is like a personal computer, but it has a more powerful microprocessor and, in general, a higher-quality monitor.

Purpose: it is a type of computer used for engineering applications (CAD/CAM), desktop publishing, software development, and other types of applications that require a moderate amount of computing power and relatively high quality graphics capabilities

Minicomputer: A multi-user computer capable of supporting up to hundreds of users simultaneously.

Purpose: A minicomputer is a midsize computer. In the past decade, the distinction between large minicomputers and small mainframes has blurred, however, as has the distinction between small minicomputers and workstations.

Mainframe: A powerful multi-user computer capable of supporting many hundreds or thousands of users simultaneously.

Purpose:  Mainframe was a term originally referring to the cabinet containing the central processor unit or "main frame" of a room-filling Stone Age batch machine.

Supercomputer: An extremely fast computer that can perform hundreds of millions of instructions per second.

Purpose: Supercomputer is a broad term for one of the fastest computers currently available. Supercomputers are very expensive and are employed for specialized applications that require immense amounts of mathematical calculations