Plugin / Script For Customized Search Suggestion

I always wondered the name of the script that is used to query suggestions based on what you type in a search field box.

I was wondering if such a plugin, or at least the name of this script type, exists.

Examples are when you type in to Google, and it suggests stuff. Or when you type a name into Facebook, and it suggests names based on the letters. Or WordPress, when you type in the tags.

Is there a name for this? Is there somehow a way to make it work for specific links within my blog ( instead of searching the entire blog )?