C++ uses name mangling to give names to non-virtual methods. They are no different than a C function that takes a pointer, except they may use a different calling convention.
Even if the method is virtual, C++ compilers make an effort to call methods directly without indirection through a vtable wherever possible.
The interesting thing is that you can't call the "function that takes a pointer". Accessing it as a method is the only thing which works.
A long term ambition for C++ and more specifically for Bjarne has been UFCS, Universal Function Call Syntax, which a few other languages have. But C++ can't do this today.
std::mem_fn will effectively give you the underlying function that takes a pointer. Strictly speaking mem_fn is defined to generate the wrapper function, but in practice the optimizer is just going to strip that away and call the name-mangled function directly.
Yup, but then the call syntax is different so it fails to achieve the "Universal Function Call Syntax" that OP was asking for which std::mem_fn provides.
To be more clear, when no "virtual" method is declared, then no table is generated because none is needed.
In this case, the addresses of all the methods are known at compile time and the compiler knows which to choose when anyone is invoked in the source code, based on the type of the object and on the types of the method arguments.
When there is at least one "virtual" method and you have a pointer to an object, the type of the object cannot be known at compile-time, so the compiler cannot determine which method to invoke.
That is why the compiler needs to create a table with pointers to the virtual methods for each class with such methods, and each object of those classes must include a pointer to the corresponding vtable, so that the correct method to invoke can be determined at run time (from the index of the virtual method).
Only classes with one or more virtual functions have virtual method table. Objects of such classes are called polymorphic objects and they (and only they) have hidden pointer to virtual method table.