Explain difference between: function Person(){}, var person = Person(), and var person = new Person()?

This question is pretty vague. My best guess at its intention is that it is asking about constructors in JavaScript. Technically speaking, function Person(){} is just a normal function declaration. The convention is to use PascalCase for functions that are intended to be used as constructors.

var person = Person() invokes the Person as a function, and not as a constructor. Invoking as such is a common mistake if it the function is intended to be used as a constructor. Typically, the constructor does not return anything, hence invoking the constructor like a normal function will return undefined and that gets assigned to the variable intended as the instance.

var person = new Person() creates an instance of the Person object using the new operator, which inherits from Person.prototype. An alternative would be to use Object.create, such as: Object.create(Person.prototype).

function Person(name) {
  this.name = name;
}

var person = Person('John');
console.log(person); // undefined
console.log(person.name); // Uncaught TypeError: Cannot read property 'name' of undefined

var person = new Person('John');
console.log(person); // Person { name: "John" }
console.log(person.name); // "john"