Operating System is the System Software that makes the Computer work. We can say that an Operating System (OS) is Software that acts as an interface between you and the hardware. It not only contains drivers used to speak the hardware's language, but also offers you a very specific graphical user interface (GUI) to control the computer.
An OS can also act as an interface (from the hardware) to the other software. A complex OS like Windows or Linux or Mac OS offers the services of an OS, but also has applications built in. Solitaire, Paint, Messenger, etc. are all applications.
Application software is the software that you install onto your Operating System. It consists of the programs that actually let you do things with your computer. These Applications are written to run under the various Operating Systems.
These include things like your word processing programs, spread sheets, email clients, web browser, games, etc. Many programs, such as most of the Microsoft Office suite of programs, are written in both Mac and Windows versions, but you still have to have the right version for your OS.
For example - Tally for Accounting, MS-Word for Word Processing etc.
So, the Operating system of a Computer is the Software that allows the Computer work. It provides the framework under which the Applications run. An operating system is the type of Computer system you have such as Window XP or Window 95, 98, Mac, etc.
The Applications are the Software that actually allows the user to do something with the Computer. Without the applications, all you can do is change settings and navigate among the folders. You can purchase its CD from a software company or download from a software company’s web site.
Examples of System Software are - Operating Systems, Language Translators etc.