When you use a subdomain the document root is public_html/subdomain. When you go to yourdomain.com the document root is public_html.
So say you have a index.html in public_html/subdomain with a link /page.html or ../page.html. If you go to subdomain.yourdomain.com it's going to look for page.html in the public_html/subdomain dir. But if you go to yourdomain.com/subdomain and click on the same link it will look for page.html in your public_html dir. Because when you go to yourdomain.com the document root is public_html.
So when using a subdomain if you want to access something that is not in the subdomain's dir you need to use a full path "http://yourdomain.com/page.html".
