Initializing a variable with function-style cast in C++

int main(){
 int a = 5; // copy initialization.

 int b(a); // direct initialization.
 int *c = new int(a); // also direct initialization, on heap.

 int d = int(a); // functional cast, also direct initialization? 
                 // or copy initialization?

 return 0;
}

I have 2 questions on this:

1 - It's not clear to me if int(a); is only a cast, or if it's also an initializer. Is d being copy initialized or is it being direct initialized? i.e is the expression equal to this:

int d = 5;

or this

int d(5);

2- I want to confirm if new int(a); is only an initializer and not a cast to int. Also want to confirm if it's direct initialization and not copy initialization.

I have read section (3) of the reference but the answer is not clear to me: https://en.cppreference.com/w/cpp/language/direct_initialization

3. initialization of a prvalue temporary (until C++17)the result object of a prvalue (since C++17) by functional cast or with a parenthesized expression list