I looked online for definitions of application, tool and utility but still cannot answer for certain what virus protection programs and anti-malware/spyware programs are called (I think they would be called utilities, but not sure). I think Registry cleaning, optimization programs would be called tools, am I right? Also, an application is basically any program, is that correct?
I think you are trying to make things too complex.
An application can be used as a tool for you or the system to do something with:
application program
?noun Computers.
a program used for a particular application (opposed to system program).
Also, applications program.
Also called application software, applications software.
http://dictionary.reference.com/browse/app...n%20program?o=0
A utility program:
?noun Computers.
system software used to perform standard operations, as sorting data or copying data from one file to another, for application programs or other system software.