Which is the correct terminology?
"Correct" being ambiguous, let's see what:
- The Standard calls it,
- The C++ gurus call it,
- The vulgus calls it.
The Standard
1 In the definition of a constructor for a class, initializers for direct and virtual base class subobjects and non-static data members can be specified by a ctor-initializer, which has the form
ctor-initializer:
: mem-initializer-list
mem-initializer-list:
mem-initializer ...opt
mem-initializer-list , mem-initializer ...opt
mem-initializer:
mem-initializer-id ( expression-list opt )
mem-initializer-id braced-init-list
mem-initializer-id:
class-or-decltype
identifier
2 In a mem-initializer-id an initial unqualified identifier is looked up in the scope of the constructor's class and, if not found in that scope, it is looked up in the scope containing the constructor's definition. [ Note: If the constructor's class contains a member with the same name as a direct or virtual base class of the class, a mem-initializer-id naming the member or base class and composed of a single identifier refers to the class member. A mem-initializer-id for the hidden base class may be specified using a qualified name. — end note ] Unless the mem-initializer-id names the constructor's class, a non-static data member of the constructor's class, or a direct or virtual base of that class, the mem-initializer is ill-formed.
It's called a mem-initializer-list: this is a technical term I won't use personally.
The C++ guru
I'm currently watching the talks given at the CppCon2018, by likes of Herb Sutter, Kate Gregory, Timur Doumler, John Lakos, ... This is available on Youtube and I suggest you watch it too.
They use the term the initialiser list. Or when it's ambiguous the member initialiser list.
Now, let's compare some search results:
+----------------+-------------+
| Google scholar | Google book |
+------------------------------+----------------+-------------+
| "member initialization list" | 59 results | 948 results |
| "member initializer list" | 34 results | 553 results |
+------------------------------+----------------+-------------+
On written media, those gurus (well, everybody can write a paper or a book, but gurus tend to write more of those) call it the member initialization list most of the time.
Common C++ programmers
Well, there's the one that don't know what this is, and there's the one I've heard call it the initialiser list. I call it the initialiser list, even when talking in my mother tongue. In French, I've heard collegues call it what would translate to the initialisation list. There's some variation then I guess.
Conclusion
Call it the initialiser list. This is the correct term for me.