Initialize vectors and std

Question 1

The notation

MyClassType a;

actually calls MyClassType's default constructor, if it has one. So yes, a vector is already initialized and ready to use. Your second snippet:

myVector = vector<myClass>();

Actually creates a new, temporary vector, which is default constructed, and then calls myVector's copy assignment operator operator=().

In this regard, C++ is different from many other languages. For example, in Java, you'd need to do MyClassType a = new MyClassType(). This is not necessary in C++. Whenever you declare a value of class type with automatic storage¹, the object is automatically default constructed. This is also true for class members. Let's say you have:

class A {
    std::vector<int> m_myVector;
};

Then there is no need to initialize m_myVector - it's done automatically whenever you instantiate an object of class A.

It's different when you allocate objects on the heap:

// Note: DON'T use raw pointers in actual code - use smart pointers instead.
// Just for illustration purposes.

// This is just a pointer to an A, it's not yet initialized.
A* myA; 

myA = new A(); 
// now myA points to a heap allocated, default constructed A object.

// Note that you can omit the default constructor's `()` and just write:
myA = new A;

Heap allocating an object is actually closer to what Java does under the hood. Anyway, when writing proper C++, you rarely need to heap allocate, and you wouldn't ever do it with a vector.

¹ Automatic storage: Put simply, anything you create in C++ without using new/delete or similar.

Question 2

Is it already initialized?

Yes (assuming this is std::vector). As with any sane class, all its constructors (including the default constructor used here) put it into a well-defined state. At this point, it's a valid, empty vector.

I should call the constructor in the following way?

That's not calling the constructor (at least, not on myVector). Constructors are called automatically during object initialisation; there's no way to call it a second time. This creates another empty vector, then copy-assigns it to myVector.

On the other hand, is it the same std::vector and vector?

Presumably, this is std::vector, dumped into the global namespace with an evil using namespace std;. To avoid doubt, confusion and potential amibiguity, you should avoid doing that, remove any rogue using-directives, and always refer to it as std::vector.

Question 3

In this case

vector<myClass> myVector;

there is no need to call default constructor separately.

You can call push_back and other methods.