NIS = Network Information Service
This server consolidates information of various types. A typical example is to coordinate user and group information across several computers. A user can log into one of any number of computers and still have the same user ID, group memberships, etc. as long as the computer can communicate with the NIS server.
NFS = Network File System
An NFS server is more or less the equivalent of a "share" in the Windows environment. One or more computers (servers) can allow other computers (clients) to access the hard drives/storage located on the server through the network. From the client computers' perspective, it's as if the storage is part of the local machine.