Final answer:
An overloaded constructor in programming is one of multiple constructors in a class that each have different signatures, allowing for the creation of objects in varying states. It isn't overloaded due to an excessive number of program statements nor does it have a different name from other constructors.
Step-by-step explanation:
An overloaded constructor refers to option 1: A second or other multiple constructor with a different signature than any other constructor. In object-oriented programming, constructors are special methods used to initialize objects. An overloaded constructor means that a class has more than one constructor, each with a unique set of parameters (its signature). This allows for the creation of objects in different states. For example, one constructor might accept a name and age, while another accepts only a name, and a default age is set.
The notion that a constructor is overloaded does not relate to having too many program statements (option 2), nor does it refer to a constructor with a different identifier (option 3), since constructors must have the same name as the class itself. Also, it's important to know that having the same heading as another constructor (option 4) is not allowed in the same class as it would cause a compilation error due to ambiguity.