That's mostly it; although in C++ the member functions (methods) of an object are the ones of that class. The code inside member functions is stored in one place, usually unaltered through the program's execution. Whenever an object wants to call a member function, it calls that code. (There's a secret argument, the 'this' pointer, which is passed with every member function. 'this' is a pointer which points to the object that "owns" the method. Hopefully that makes things clearer...)
Is it really that simple? If the constructor were a part of the object, how could it be used to construct that very object ?
The egg or the chicken ?
However, thats just a theoretical problem, if at all. Basically it's correct: You use the constructor to create the object.
I don't know if there is an explanation for it in C++. In Delphi you always call a constructor as "a method of a class", therefore it's not really part of the object [like instance = classname.constructorname(parameter)].