Of late, many mainstream distributions have been switching to SystemD as their init system. This includes Debian (since Debian 8) and Ubuntu (since Ubuntu 15.04). In the traditional SysV init system we used to have stuff like spawn-fcgi or custom scripts for starting a FastCGI process and having the web server connect to it over Unix or TCP sockets. Such kind of usage decreased when PHP FPM was introduced since it’s safe enough to assume that 90% (probably more) of the FastCGI deployments are just launching PHP interpreters using whatever mechanism is there (spawn-fcgi or custom scripts). PHP FPM does this for you now and it’s pretty good at it.
FastCGI is just a protocol, it can be used by any application. For custom applications which do not support starting their own FastCGI processes and listening on a socket we have to use external mechanisms. SystemD has a couple of good features which can help reduce the amount of custom work needed in terms of process monitoring, socket paths, file ownership, etc.