There are three kinds of 'servers' - forking, threading and single threaded (non-blocking). All of them generally loop the way you show, the difference is what happens when there is something to be serviced.
A forking service is just that. For every request, fork() is invoked creating a new child process that handles the request, then exits (or remains alive, to handle subsequent requests, depending on the design).
A threading service is like a forking service, but instead of a whole new process, a new thread is created to serve the request. Like forks, sometimes threads stay around to handle subsequent requests. The difference in performance and footprint is simply the difference of threads vs forks. Depending on the memory usage that is not servicing a client (and prone to changing), its usually better to not clone the entire address space. The only added complexity here is synchronization.
A single process (aka single threaded) server will fork only once to daemonize. It will not spawn new threads, it will not spawn child processes. It will continue to poll() the socket to find out when the file descriptor is ready to receive data, or has data available to be processed. Data for each connection is kept in its own structure, identified by various states (writing, waiting for ACK, reading, closing, etc). This can be an extremely efficient design, if done properly. Instead of having multiple children or threads blocking while waiting to do work, you have a single process and event loop servicing requests as they are ready.
There are instances where single threaded services spawn multiple threads, however the additional threads aren't working on servicing incoming requests, one might (for instance) set up a local socket in a thread that allows an administrator to obtain a status of all connections.
A little googling for non blocking http server will yield some interesting hand rolled web servers written as code golf challenges.
In short, the difference is what happens once the endless loop is entered, not just the endless loop :)