How does CGI, FastCGI, WSGI work?

Question

FastCGI

Hello. I wanted to clarify whether I correctly understand the difference between the above protocols.
1) The CGI script is on the same server as the server. The server launches the CGI script, passing it query parameters to the environment variables, and passes the data from the script output stream to the user.
2) FastCGI application has an internal socket implementation, so it can be run on a different server than the web server itself. FastCGI application handles all the logic and sends the result through the
socket
There is a server that simply accepts an http request, parses it, separating the header and body, and then calls the function described in the config, passing the request components there. The site developer writes the same function. This function handles all the logic and returns a response in a specific format.
The question, in fact, sounds like this:
Is the above correct?