Both, accessing a property that isn't defined on an object and a property that contains the primitive undefined value, will return you undefined.
For example:
var obj = {
  a: undefined
};
obj.a; // undefined
obj.b; // undefined
The difference is that a is an own property, and b isn't:
obj.hasOwnProperty('a'); // true
obj.hasOwnProperty('b'); // false
In the first case a is an own property, even if it contains undefined as its value. In the second case, b is not an own property, accessing obj.b will look for a property named b, all way up in the prototype chain.
When the prototype chain ends (when it reaches an object with a null [[Prototype]]), the property lookup ends and undefined is explicitly returned.
You should know that the hasOwnProperty method checks only if the property physically exist on the object (own properties), but we have also inherited properties, for that case we can use the in operator, for example:
function Test () {}
Test.prototype.a = 'foo'; // instances of Test will inherit from Test.prototype
var obj = new Test(); // { a="foo",  b="bar"}
obj.b = 'bar';
obj.hasOwnProperty('a');  // false
'a' in obj;               // true
obj.a;                    // 'foo'
obj.hasOwnProperty('b');  // true
As you can see, obj inherits from Test.prototype, and the a property is not an own property, but it is available through the prototype chain. That's why hasOwnProperty returns false and the in operator returns true.
You can see how internally properties are resolved by the [[Get]] internal operation
Notes:
- Accessing undefinedas an identifier is not considered to be safe on ECMAScript 3 (the most widely implemented version of the language standard), because instead of being a language keyword (such asnullfor example) is just a property of the global object, and it is writable on this version of the Spec., meaning that if someone replaces its value (e.g.window.undefined = 'LOL';) , it will break your code.
The typeof operator as @strager mentions can be used instead, for example:
if (typeof obj.prop == 'undefined') { /*....*/ }
This operator returns always a string (it's safe to use == :), and its value depends of the type of its operand, the possible values are described here.
Another common way to solve this is to declare your own undefined variable, available on the scope of your functions, for example, some libraries use the following pattern:
(function(undefined) {
  // code here
})();
The function has an argument named undefined, and it is executed immediately without passing any value to it (the last pair or parens make the invocation).
Maybe is worth mentioning that the undefined global property was finally described on ECMAScript 5 as non-writable (immutable, as well non-enumerable and non-configurable -non deletable-).
- Using the - hasOwnPropertymethod directly from an object instance is also not considered as safe, because if some object has a property with the same name, the original method will be shadowed. For example:
 - var obj = { hasOwnProperty: function () { /* evil code :) */ } };
 
If you call:
    obj.hasOwnProperty('prop'); 
The method defined on the object will be executed (and you wouldn't want this since you know exactly which method you want to invoke...), because it shadows the one from the Object.prototype, however it can be safely invoked by:
    Object.prototype.hasOwnProperty.call(obj, 'prop');