DHCP serves up IP addresses for new computers on your network (if you do not hardcode them). This is usually handled by your router, although Mac server does have a DHCP server.
A Name Server is the computer that handles DNS. Again, Mac server has a DNS server you can activate.
Usually, your ISP (via DHCP on the WAN side) give your router DNS servers to use when it gives your router its WAN IP address. so you can point to your router, but those DNS servers won't know about your private network.