Your understanding is correct, if you're from the past. You're pretty much describe as it looked like in 1990s.
Yes, many languages can be executed directly by a web server plugin. Right on for PHP, mod_php for Apache is still the most popular way to host it. However, high-traffic sites use more modern approach, using web server only as a proxy for FastCGI (in case of PHP it's PHP-FPM)
the output is embed into HTML pages is then sent back to the client.
I think you're referring to early 90's so called spaghetti code, however modern approach is to use one of many MVC frameworks. In case of PHP that would mean for example Zend Framework (there are numerous alternatives).
As for ASP, you're probably referring to so called "classic ASP", which is obsolete. Currently it's ASP.NET, which can use any of .NET languages (C# being the most popular), and of course the .NET framework.
C and C++ are not typically used for web application. If so, such services are implemented either as stand alone servers, as module for web server or as FastCGI.
Perl can be executed directly from web serve module using mod_perl. There is also PSGI, which is basically clone of Python's WSGI.
Python is very popular language for web apps. It can be directly executed from Apache web server via mod_python, however that is obsolete and not recommended. Currently the way to go with Python is either via WSGI server module. WSGI server implemented in Python (eg. CherryPy, WebPy) or using stand alone Python web stack (Tornado and Twisted's Web module are fine examples). And of course again, you'd most probably will be using WSGI compatible MVC framework, Django is the most popular one (again, multiple alternatives available).
Ruby, again very popular language for web apps. Best known for web framework Ruby on Rails, which again is MVC. You can execute Ruby directly from server module via mod_ruby or via FastCGI.
Servlets/JSP are executed in stand-alone J2EE application servers, such as JBoss or Tomcat. It's more commonly used to add web interface to business system rather than to create stand alone web apps.
Classical CGI (ie. spawning process on each request) has become obsolete many years ago. It has been replaced by FastCGI (where process is long-running, rather than spawned on each request), server modules, interfaces such as WSGI and clones and stand-alone solutions.
Also the paradigm of the request processing has evolved, with CGI it was process per request. Then was process pool (or thread pool), each process (thread) handling one request at a time. However now, most modern approach is for web servers and stand-alone frameworks to use event-driven programming.
The main difference is that syntax is grammar defined in a language to allow you to expose some functionality. As soon as you could get to that functionality, any other syntax that lets you do the same thing is considered sugar. That of course runs into odd scenarios about which of the two syntaxes is the sugar, especially since it's not always clear which came first.
In practice, syntactic sugar is only used to describe syntax added to a language to facilitate ease of use, like making infix lhs + rhs map to lhs.Add(rhs). I would consider C's array indexing to be syntactic sugar.
It matters mostly because elegant designs tend to limit the amount of duplication. Needing (or at least wanting) syntactic sugar is seen by some as a sign of a design failing.
Best Answer
Basically the difference is just one of degree. A script tends to be a lot more formally defined, with a well-defined scripting language behind it, while a macro is usually something more simple and ad-hoc. Macros are frequently "recorded" by telling a program "watch everything that I do" and then performing the action, whereas scripts are generally entered as text in the scripting language.