I would argue that the defining characteristic of a scripting language is the ability to execute scripts instead of generate binaries. You could then make a further distinctions between application scripting languages (the origin of Lua and Javascript) and general-purpose scripting languages (which are independent of a host application - think Perl or Python).

This distinction is not sharp: Today, Lua and Javascript are used as general-purpose scripting languages, people ship 'fakecutables', packaging script and runtime system into a binary, and even C++ has been used to script applications (physicists are silly people ;)).

But there's normally still a dominant usage pattern associated with a given language, so the classification is not entire useless.