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.
I needed WordPress to return the path for a given post because it was easier to migrate WordPress installations across different domains, as there would be no broken internal links. For example, migrating from a development internal site, to a production live site.