Yes, "server" is not really a good description. It's the server side of the equation, but the server is a client of the FastCGI protocol, in that the server requests and the FastCGI app responds. This is the same problem with X terminology.
Really we should have words that mean closer to human/user and further from human/user, because this is often what we are really concerned about, or can most easily understand when considering the architecture. Note that developers don't count as humans in this equation ;)