Both cases refer to the same name, the ".name" vs "name/" convention is just a reference to how you can use your name. For instance, if you own "nakamoto" on Handshake, you can use "nakamoto" as a domain itself. In that case, you would point "nakamoto" to your website and visit it at http://nakamoto/ in your browser. You can also use "nakamoto" as a TLD and issue your own subdomains. In that case you can create "satoshi.nakamoto" and visit it at http://satoshi.nakamoto in your browser. A Handshake name can be used as both a domain name directly and as a TLD at the same time.