This might give you a broader understanding of their difference:
CGI: (common gateway interface) It is a specification "protocol" for transferring information between a Web server and a CGI program.
A CGI program is any program designed to accept and return data that conforms to the CGI specification.
Basically it‘s a way to run a server side script (PHP, Perl, Python,...) when a HTTP request comes.
CGI is very slow in comparison to other alternatives.
FastCGI: is a better CGI.
Fast CGI is a different approach with much faster results.
It is a CGI with only a few extensions.
FastCGI implementation isn’t available anymore, in favor of the PHP-FPM.
PHP-FPM: (FastCGI Process Manager), it‘s a better FastCGI implementation than the old FastCGI.
It runs as a standalone FastCGI server.
In general it‘s a PHP interface for the web servers (Apache, Nginx..) to allows Web Server to interact with PHP.
Unlike the PHP-CLI which is a command line interface for PHP to allows Users to interact with PHP via terminal.
mod_php: an Apache module to run PHP.
It execute PHP scripts inside the Web Server directly as part of the web server without communicating with a CGI program.
mod_SuPHP: is similar to mod_php but can change the user/group that the process runs under.
Basically it address some problems of mod_php related to permissions.
原文地址：https://www.cnblogs.com/kidsitcn/p/10506816.html