cliche

They're only exactly the same for theorems you can prove a priori - ie those which are necessarily true.
ie in all possible worlds, 2+2=4 (assuming we are taking all to be 'all logically possible'). You can prove that without any reference to the world itself - it is 'a priori' and therefore necessarily true; true in all the worlds.
A fact like "grass is green" cannot be proven by simply using the axioms of the system - you must refer to the possible world itself; ie "grass is green" is true iff grass is green. It is only true in a limited subset of possible worlds.
So "necessary" statements are true in all possible worlds, whereas "possible" ones are only true in some - so they're not all the same.

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I can't understand why people are frightened of new ideas. I'm frightened of the old ones. -- John Cage (1912 - 1992)