First, it'd be useless to talk about the distinction between a "scripting language' and a 'programming language', because it's clear that the same language can be used in different contexts and environments, be interpreted in some cases or compiled in others.
The only distinction worth discussing in my opinion is whether a portion of source code is a script or a program.
A very easy conclusion can be found in "Building Skills in Python", S. F. Lott:
The “scripting” distinction is an operational feature of POSIX-compliant operating systems. Files which begin with the ‘#!/path/to/interpreter’ will be used as scripts by the OS. They can be executed from the command-line because the interpreter is named in the first line of the file.
Languages like Java, C and C++ do not have this feature; these files must be compiled before they can be executed.
So what happens if you have, say, a couple of thousands lines of Perl code, distributed in about a hundred classes, using a few CPAN modules?
It'll be interpreted, not compiled, but would you present it as a script? I don't think so.
Also, the "shebang" (#!/path/to/interpreter) is not really the point, is it? You can omit it and then specify which interpreter has to be used and still have an interpreted execution.
See this other definition (Think Python - How to Think Like a Computer Scientist, A. Downey):
script: A program stored in a file (usually one that will be interpreted)
As superficial as this may seem, I think this is actually getting to the point, so here comes my personal definition of "script":
A script is a sequence of instructions, stored in a file, which can be directly executed by an interpreter.
Of course this has be taken in an honest and pragmatic way. A good software developer won't put the thousands of lines of Perl mentioned above in a single file, even if it's absolutely legal.
When a script starts to become so big (say more than a page? - 200 lines of code or so) to require the inclusion of other files, depending on my definition that becomes a program, even if it's still interpreted.
What do you think?