Select the public/private push button to toggle between public and private methods for selected categories.

Whether a method is public or private does not affect its behavior. Making your method public or private is merely a way of categorizing it (other than placing it in a category). A popular convention is to make a method public if other parts (or classes) use it, and make it private if only the class that contains it uses it.

The push button is located below the Scripts list (upper-right) pane of the Script Editor.