Hey @Dimitris_Derm. ,
I still do not 100% follow what you are saying and asking, which likely means that you or I are misunderstanding something.
What are Commands?
Cinema 4D is built itself on the same plugin architecture offered to third parties. There are many plugin types in Cinema 4D, but a central one is CommandData. A command is an operation that can be invoked without any arguments except the plugin ID of the command to invoke (and optionally a sub ID). CallComand is the function to call commands by their command/plugin ID. I.e., when you implement a command plugin as a user, everyone can call it via its command ID. Commands in this sense are not to be confused with modelling or uv commands, which are a different thing.
Almost all buttons and menu entries in Cinema 4D are commands. So, when you for example implement an ObjectData 'Plane' plugin and register it, Cinema 4D will create a hidden CommandData plugin for you, so that this object can be created from a menu. Here shown with the builtin 'Plane' object:

What are Symbols?
The raw integer values for plugin IDs are usually (but not always) aliased with a 'symbol'. Symbol is just programmer slang for an alphanumeric label under which some data is accessible. E.g., foo, bar, and baz below are symbols:
foo: int = 123456
bar: dict[str, float] = {"Hello": 1.0, "World": 2.0}
baz: callable = lambda x: x * 2
In C(++), the langauge Cinema 4D is written in, the word symbol is very common. In the Cinema API it always refers to some alpha-numeric label for some integer value. There is code which is shipped to customers (the public APIs) and there is code that is internal. In order not to have users use raw integer values, we have to define such symbol, i.e., alias in the public API. This does not always happen.
What is the Script Log doing?
The script log is just a series of the the commands being called. There are no classes, functions, or methods. In some cases the script log creates more complex code (for tools), but the script log is never a place to learn the API, as it only operates via command IDs. And the script log uses the raw integer values because for once there is not always a symbol, and it would also not be trivial to access the symbol for each command from the C++ code that generates the log.

Cheers,
Ferdinand
PS:
By "method" I meant the programmatic term which some times coincides with the term "function".
I understood that, but just as a clarification, method and function are not synonymous. A method is a function that is associated with an object (i.e., it is a member of a class). A function is a more general term that can refer to any callable piece of code, including methods, but also standalone functions that are not associated with any object.