Perhaps they are synonyms or perhaps they carry different meanings to categorize the various 'installed tools' on a computer. I'd like to clarify.
closed as not constructive by KronoS, studiohack♦ Jun 23 '12 at 0:29
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There are no universally applicable hard definitions for these things.
A program used to be a single binary executable file, perhaps with associated library files and most likely dependent on shared libraries provided with the operating system (or with a specific run-time environment provided with, or installed on, the operating system.
An application is typically something the end-user sees as a single coherent thing for carrying out a certain category of tasks. Most applications consist of a single program but it is possible that an application consists of a set of programs. The multiplicity of programs may be invisible to the user (because the programs call each other) - or may be apparent.
Sometimes, applications are sold as an application-suite if the separate parts are also marketed individually or have a clearly separate identity. For example: Microsoft Office.
Programs and applications are software.
The above is subjective. Others will have different views. There is no single "correct" definition. These terms get used by marketing folk (and therefore all bets are off, logic has no say)
Example of software: MS Office.
Example of an application: MS Excel, MS Word, etc.
An application requires the software to be installed to work, so that the system recognizes the commands set up in the application.