100% sure: Sam isn't hungry.
99% sure: Sam couldn't be hungry.
99% sure: Sam can't be hungry.
95% sure: Sam must not be hungry.
Less than 50% sure:
Sam may not be hungry.
Sam might not be hungry.
(a) Sam doesn't want anything to eat. He isn't hungry. He told me his stomach is full. He says he isn't hungry. I believe him.
In (a): The speaker is sure that Sam is not hungry.
(b) Sam couldn't be hungry.! That's impossible! I just saw him eat a huge meal. He has already eaten enough to fill two grown men. Did he really say he'd like something to eat? I don't believe it.
In (b): The speaker believes that there is no possibility that Sam is hungry (but the speaker is not 100% sure). Notice the negative use:
couldn't and can't forcefully express the idea that the speaker believes something is impossible.
(c) Sam isn't eating his food. He must not be hungry. That's the only reason I can think of.
In (c): The speaker is expressing a logical conclusion, a "best guess."
(d) I don't know why Sam isn't eating his food. He may/might not be hungry right now. Or maybe he doesn't feel well. Or perhaps he ate just before he got here. Who knows?
In (d): The speaker uses may not/might not to mention a possibility.