This is an interesting topic, and I don't think there are very good guidelines for the differentiating a "script" and a "application."
Let's take a look at some Wikipedia articles to get a feel of the distinction.
Script (Wikipedia -> Scripting language):
A scripting language, script language or extension language, is a programming language that controls a software application. "Scripts" are often treated as distinct from "programs", which execute independently from any other application. At the same time they are distinct from the core code of the application, which is usually written in a different language, and by being accessible to the end user they enable the behavior of the application to be adapted to the user's needs.
Application (Wikipedia -> Application software -> Terminology)
In computer science, an application is a computer program designed to help people perform a certain type of work. An application thus differs from an operating system (which runs a computer), a utility (which performs maintenance or general-purpose chores), and a programming language (with which computer programs are created). Depending on the work for which it was designed, an application can manipulate text, numbers, graphics, or a combination of these elements.
Reading the above entries seems to suggest that the distinction is that a script is "hosted" by another piece of software, while an application is not. I suppose that can be argued, such as shell scripts controlling the behavior of the shell, and perl scripts controlling the behavior of the interpreter to perform desired operations. (I feel this may be a little bit of a stretch, so I may not completely agree with it.)
When it comes down to it, it is in my opinion that the colloquial distinction can be made in terms of the scale of the program. Scripts are generally smaller in scale when compared to applications.
Also, in terms of the purpose, a script generally performs tasks that needs taken care of, say for example, build scripts that produce multiple release versions for a certain piece of software. On the otherhand, applications are geared toward providing functionality that is more refined and geared toward an end user. For example, Notepad or Firefox.