The first/
in IIS refers to the root folder of the domain/localhost. For example, you can access the page with your browser like this: http://localhost/path/file.php
The second form, without the /
means that the URL is relative from the folder of the page that includes file.php go to sub-folder path and there find the file.
I believe that the folder structure is different between the machines: on the unix machine, it's deployed under: http://www.youdomain.com/somefolder/HERE