How does instanceof work in JavaScript?

What is the best way to recognize that obj2 and obj3 are different?

That will depend a great deal on what you're doing with them. One way would be to use instanceof Obj2 and instanceof Obj3. Since both objects were created with Obj1.prototype in their prototype chain, it makes sense that they identify as being an instance of what we would call the supertype in class-based OOP.

How does actually instanceof work?

The short version

obj instanceof F looks to see if the object referenced by F.prototype is anywhere in obj's prototype chain. It doesn't use constructor at all.

More details

This is covered in the spec by §11.8.5 - The instanceof Operator, which says (indirectly, via §8.6.2) that it calls the [[HasInstance]] internal method of the function object, passing in the object we're testing. Function's [[HasInstance]] (in §15.3.5.3) says that it gets the object reference from the function's prototype property and then returns true if that object is anywhere in the target object's prototype chain, false if it doesn't.

It doesn't use constructor (nothing in JavaScript itself does, in fact) — and if you think about it, it can't, because an object's constructor property can only point at one function, but an object can be instanceof multiple functions — for instance, in the case of pseudo-classical inheritance:

function F1() {}

function F2() {
  F1.call(this);
}
F2.prototype = Object.create(F1.prototype);
F2.prototype.constructor = F2;

var obj = new F2();
console.log(obj instanceof F1); // true
console.log(obj instanceof F2); // true

Both are true because the two objects referenced by F1.prototype and F2.prototype are both in obj's prototype chain.

instanceof being true doesn't necessarily mean that obj was created by a call to F, either directly or indirectly; it just indicates there's a vague link between them (F.prototype refers to an object that's also in obj's prototype chain). It usually means F was involved in creating the object, but there's no guarantee.

For instance:

function F() {}
var obj = Object.create(F.prototype);
console.log(obj instanceof F); // true

Note that F wasn't called to create the object, at all.

Or perhaps more clearly and/or dramatically:

function F() {}
var p = {};
var obj = Object.create(p);
console.log(obj instanceof F); // false
F.prototype = p;
console.log(obj instanceof F); // true

There's also this unusual, but entirely possible, version:

function F1() {}
function F2() {}
F1.prototype = F2.prototype = {};
var obj = new F1();
console.log(obj instanceof F2); // true

Or this one:

function F1() {}
function F2() {}
var obj = new F2();
console.log(obj instanceof F1); // false
F1.prototype = F2.prototype;
console.log(obj instanceof F1); // true

Most simply: obj instanceof constructor yields true when obj has constructor's prototype in it's constructor/prototype chain. In other words, your asking your engine whether obj can be treated like an instance of constructor / whether obj behaves like a constructor object.

There is a small handful of syntaxes that allow you to put constructor's prototype in obj's prototype chain. Any and all of them will cause obj instanceof constructor to be true. In your examples, both obj2 and obj3 have Obj1 in their prototype chain.

So, when you ask your javascript engine whether either obj2 or obj3 behave like an instance of Obj1, JavaScript assumes true -- the only case wherein they wouldn't is if you've overridden Obj1's behavior down the line.