So basically, you are asking about the difference between
Either one will work. In the former example, a web server will go to example.com and look for a file named "stage". If it can't find that file, it will look for a directory with that name, and look for an index file.
In the latter example, the server will automatically go the directory named "stage" and look for an index file. It saves a bit of overhead on the server, which is important if you have a lot of traffic.
I'm not quite sure what you mean by "the domain selection tool". If you are talking about a one-click install, "stage" alone will suffice.