Magic Wand Icon

What is the origin and meaning behind the magic wand icon? I've seen it in a bunch of programs and they all seem to have different functions.

In Photoshop it is used a:

"tool that selects similarly colored areas"

In Prism 6 it is used as:

“Magic”, which stands for Make Graphs Consistent.

So is it just a tool icon that's used for a number of different purposes which are just too specific to have a more related icon?