Question

Can i call a member template, template template member function? or how can I know to call it member template and how does it make sense?

For example:

For case A: I have a class, if I make its member function a template member function, would i call it a member template?

For case B: I have a template class, If I make its template member function a template, would I call it a member template or can I call it template template member function?

Answer 1

For both cases you call it member template.

template<typename T>
struct A {
  // this is not a template
  void f();

  // but this is a member template
  template<typename T> void g();
};

It’s a member template because it’s a member that is a template. The member function f is not a template, but is a member function of a class template. In C++ there is unfortunately not a clear terminology for such a thing, so it happens that certain rules are formulated in the Standard to apply for templates, but are intended to apply also for member functions of class templates. And many rules need to enlist all the joyful combinations like

function template
member function of class template
member function of nested class of a class template
member function template 
...

Same applies for member classes of class templates. It has been proposed to call member functions/classes of class templates temploid or something like that. Work is under way to fix this state of affairs, though.