Please, tell me the difference between these two statements.
Able to technically describes your ability to do something, while can means that you are not only capable of doing a certain action, but also that you are allowed to do such an action.
Imagine the following case:
I can swim.
This means that you know how to swim and also you are allowed to go to the pool and swim. Your parents are OK with it.
I am able to swim.
This means that you know how to swim, but doesn't further specify whether you are allowed to swim. Maybe you are not. Maybe your parents did not allow you to, because they are worried you'd drown.
Therefore, a great sentence would be:
I am able to kill a man, but I can't do it.