Strips off the domain name and leaves the path and query string when you click on "Get Shortlink"
Shortlinks By Path hooks into the WordPress filter
get_shortlink to only return the path for a shortlink. This makes it easier to retrieve the shortlink url with an absolute path minus the domain name.
By default WordPress returns the full path to your post when clicking "Get Shortlink". Shortlinks By Path returns only the path. For example, by default WordPress would return
http://blog.aizatto.com/?p=3565 , with Shortlinks By Path enabled WordPress returns