If you leave off the domain, then the computer is going to assume you mean it's on the same domain. So if you have a page in the main folder of your adopts site, the inc/functions.php is all that's needed to access the functions file. However if you're on a page in the inc folder, you cannot get back to the main folder without using the domain. It's only if you're in the same folder or if the folder is contained within the folder you're in. I'm sorry if that did not make any sense.

EDIT:
Think of it as one-way doors(folders) with boxes(files). If you're in a folder, you can access any of the boxes there, or you can go through other one-way doors to see the boxes in those rooms. However you can't go backwards, you have to start all over from the beginning if you want to go back. XD

Ok thanks for that explanation ill play around with it but i think it makes sense.