I tend to think of a script as a small program that runs without user interaction and an application as something that requires someone to help it along. So a log parser or backup program that runs as a cron job is a script and a mail program is an application. On the same thought sendmail is not a script but an application because even though it doesn't require direct input it gets input from whatever other program is using it.

However this is a huge generalization and they tend to be pretty much worthless in the real world. (:

requisite obfuscation sig below:
perl -e 's;;uoli;;$a=length;y;g-w;e-u;;;$a--;s;j;$a;;print"$_\n";'