What is the difference between necessary and synthetic truths?

The distinction between necessary and synthetic statements is an ontological distinction. We can discern between statements which would hold in all possible worlds, and ones which could be rendered false if the state of affairs were to be slightly different. Let us take the example of Pythagoras' theorem; where A and B represent the lengths of the adjacent and opposite sides of a right-angled triangle, and C the hypotenuse, the sum of the lengths of A and B squared is equal to the length of C squared. Mathematicians have done much work to prove this idea geometrically. Even if the state of the world was different, this rule would still hold. As Pythagoras' theorem holds true in all possible worlds, it is an example of a necessary truth. Now let us consider, 'my laptop is silver'. It is simple to conceive of a possible world where I happened to choose a gold laptop, or not purchase a laptop at all. In other possible worlds the statement can easily be rendered false, making the proposition synthetic. It is not necessary that my laptop is silver, it just happens to be the case in this state of the world.