Don't forget the ordinary UNIX domain socket: you can think of them like TCP connections bound to 127.0.0.1 but not assigned a port number but a path name. This can be useful if you have e.g. 3 instances of the same program that needs to do some client/server work: rather than figuring out a port number assignment it can have a UNIX socket. Linux has also an extension to this mechanism, where the UNIX socket does not create a corresponding file.

In addition to doing cool things like passing open files over a UNIX socket, or credentials (your remote server can verify the UID of whoever opened the file in the other end!) the SOCK_DGRAM UNIX sockets are reliable and accept packets beyond normal UDP limits. This is useful for load balancing (you don't have to proxy your connection but can pass the new accepted socket directly to whowever is going to send data to it).

So if you want to make a simple server yet requesting/replying good size packets you can bind it to AF_LOCAL/SOCK_DGRAM, then the client calls bind() and sendto() while the server calls bind, then recvfrom() (which fills in the address of the caller) and sendto() back.