JavaScript prototype inheritance cases

In the first snippet, you're not storing your methods in the Parent's prototype, so cloning Parent's prototype for the Child class isn't doing anything. You're still able to call parentFoo from the child instances because you're running the parent constructor with the child as its context with Parent.apply(this, arguments); which runs

this.parentFoo = function() {
   //...
}

where the context this refers to the child instance.

I'm pretty sure re-defining and binding your methods in the constructor is not optimal.

In the second snippet, you're calling the constructor of the parent on the child, but you're not extending the parents prototype on the child class, so you won't be able to access the parentFoo method with instances of the child. You could fix that by adding the line from the first snippet:

Child.prototype = Object.create(Parent.prototype);

Edit: The difference between the two cases is in the first one, you're not using prototypical inheritence. You are cloning the parent prototype into the child's prototype, but you're not attaching any keys to the parent prototype. Instead you're redefining and directly binding each method to the instance in the parent constructor when you call Parent.apply(this, arguments); in the child's constructor.

I believe the difference is the latter option (prototype) adds it to the signature of the object, but the former (using this) adds the function as a part of the memory footprint of the object. Therefore, in the latter option, the Parent object has parentFoo as part of it's definition, but in the former, each instance of the parent object has that function in memory.

See Learning JavaScript, especially class-like Constructor function and Property Inheritance through prototype/proto chaining and References therein.

Inheritance in JavaScript is usually done by Child.prototype=new Parent();.

// 'function' has "prototype" property by default.
// 'object' including 'function object' has "__proto__" property by default.

function Employee(){
   // Implicitly "this.__proto__=Employee.prototype;"
   this.name="empty";
   this.dept="general";
}
// By default, "Employee.prototype={__proto__:Object.prototype}"
// "(new Employee)={__proto__:Employee.prototype, name:"empty", dept:"general"}"
Employee.prototype.a="This is 'a' in Employee.prototype"; // Additional prototype 'a'.
// Then, "Employee.prototype={__proto__:Object.prototype, a:"Employee.prototype.a"}"


function Manager(){
   // Implicitly "this.__proto__=Manager.prototype;"
   this.reports=[];
}
// "(new Manager)={__proto__:Manager.prototype, reports:[]}"
Manager.prototype=new Employee;
// Then, "Manager.prototype={__proto__:Employee.prototype, name:"empty", dept:"general"}"

function WorkerBee(){
   // Implicitly "this.__proto__=WorkerBee.prototype;"
   this.projects=[];
}
// "(new WorkerBee)={__proto__:WorkerBee.prototype, projects:[]}"
WorkerBee.prototype=new Employee;
// Then, "WorkerBee.prototype={__proto__:Employee.prototype, name:"empty", dept:"general"}"


function SalesPerson(){
   // Implicitly "this.__proto__=SalesPerson.prototype;"
   this.dept="sales";
   this.quota=100;
}
// "(new SalesPerson)={__proto__:SalesPerson.prototype, dept:"sales", quota:100}"
SalesPerson.prototype=new WorkerBee;
// Then, "SalesPerson.prototype={__proto__:WorkerBee.prototype, projects:[]}"

function Engineer(){
   // Implicitly "this.__proto__=Engineer.prototype;"
   this.dept="engineering";
   this.machine="machine";
}
// "(new Engineer)={__proto__:Engineer.prototype, dept:"engineering", machine:""}"
Engineer.prototype=new WorkerBee;
// Then, "Engineer.prototype={__proto__:WorkerBee.prototype, projects:[]}"