What's the difference between the two sentences:
You can not eat that
You must not eat that
While they could be used for anything where eating the object is forbidden, on their own "You can not eat that" would be applicable to things that you literally could not eat (Like a rock, or a plate of food too large for you to stomach), while "You must not eat that" is more applicable to something that is wholly edible, but forbidden.
"Cannot" has connotations regarding ability, while "must not" is more about authority and requirements.
Perhaps some examples would help.
You can't eat that (because it's physically impossible):
You mustn't eat that (because doing so would be wrong or inappropriate):
You can't eat that (without suffering health consequences), therefore you mustn't eat that:
The meaning is actually quite similar. In both sentences the speaker is telling the addressee that eating that food is a bad idea. More specifically:
You can not eat that: It may imply a prohibition, e.g. as in a mother to her child. But it could also mean that the speaker does not necessarily have authority over the addressee, e.g. as in a friend to another friend (one telling the other not to eat chocolate because he has diabetes).
You must not eat that: It definitely implies a prohibition uttered by a speaker who has the authority to forbid the addressee to do that action (see mother/child example above).
Generally speaking, must not sounds much more constraining than can not ('authority' is the key word). Saying "You can not" might as well sound like simply stating a fact rather than giving an order.