DNS -- Domain Name Service. This is the address lookup (phonebook) system for the internet (Web). It relates an IP address with a domain name and propagates that information around the world, so that everyone who wants to look up
www.google.com can get an IP route (74.125.93.106) to the right systems that will respond to the packet. You generally need DNS to use most web services. Some larger internal networks use DNS as well to resolve names inside of the LAN. Small home networks like mine use other services to resolve names inside my LAN.
NetBios -- this is part of MS LAN Manager IP protocol stack, it's one of the ways that systems can resolve a network IP to a server name using the CIFS/SMB protocol. You don't need DNS in this case.
I'm not a network guru, but that's my take on it. I'm sure others will add their corrections.
In a nutshell, your website won't and probably shouldn't use netbios (I don't think it routes...but I'm not sure). You would only use it for internal network SMB traffic.