"NFS" is a network filesystem that's been around for decades. Wikipedia has you covered on that front.

"VFS" is a more generic term that simply means "virtual filesystem". Within the context of Linux, it refers to the part of the kernel with which your user-space programs actually interact when they interact with "files". The VFS layer then passes requests to a concrete filesystem driver -- such as NFS, for example, or ext4, or others.

Read more here and here.

A virtual file system (VFS) is an abstraction layer on top of a more concrete file system.The purpose of a VFS is to allow client applications to access different types of concrete file systems in a uniform way, Where as Network File System (NFS) is a distributed file system protocol originally developed by Sun Microsystem in 1984, allowing a user on a client computer to access files over a computer network much more like local storage is accessed

A VFS can be used to access local and network storage devices transparently without the client application noticing the difference. It can be used to bridge the differences in Windows, Mac and Unix file systems, so that applications can access files on local file systems of those types without having to know what type of file system they are accessing Where as, NFS like many other protocols, builds on the Open Newtork Computing Remote Procedure Call (ONC RPC) system. The NFS is an open standard defined in Request for comments (RFC), allowing anyone to implement the protocol.

"VFS" is the name given to the entire layer in the kernel situated between the system calls and the filesystem drivers; it is not a filesystem in its own right.