The reason for enabling the scripting language is to allow users to customize the behavior without having to recompile the code.
I am not sure what you are asking in the second part of the question. Are you asking what other languages are used, or are you asking in what ways languages like Lua are used?
If you asked which other languages are suitable for this, one of these languages is Tcl. Tcl was designed from the ground up to be a built-in scripting language, and is very mature and reliable and easily recognizable by non-technical people.
As for which scripting languages are suitable for ... configuration files, this is one way. Using a programming language rather than a text file with name / value pairs, it allows users to add logic to their startup files. For example, you might be allowing users to assign different functions to the keys on the keyboard; with a programming language, they can add different functions for different computers. Or, if you create the game as an RPG, perhaps you can assign different keys to different character classes. If you play as a mage, F12 may be a spell, but if you play as a f12 warrior, you may have to take the final blow.
There are many ways to use scripting languages and many different languages. It all boils down to allowing your users to customize the behavior of the game without recompiling the code.
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