Hi D.W.,
Welcome to E-Learning Heroes! The difference is that a .story file is an actual project file. You can use it to create multiple projects—you'll just need to "Save As" and choose a different file name each time. On the other hand, .storytemplate files can be used over and over again to create new projects; each time you launch a .storytemplate, a new project file is automatically created. You can learn more about templates in this tutorial/video: community.articulate.com/.../using-and-creating-storyline-templates.aspx
If you click the blue "Download this file" bar at the top of this page, you'll get a .storytemplate file.
I hope that helps!