Consider the following:
He will be able to do it.
He can do it.
They mean the same thing, right?
Can "can" replace "will be able to" in any sentence? What is the difference, if anything? Why not just use the shorter version?
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No, they're not the same thing.
Will be able to obviously talks about a future event, while can talks about the present.
I can swim, so we should go to the pool.
Means I can swim already, I learned it before and I'm capable of doing it now.
I will be able to swim sometime in the future, as long as I take swimming lessons.
Means I cannot swim right now, but I'm hoping to learn in the future.
Probably you meant to ask the difference between can and am able to. If so, there is a difference, yes. Let me explain:
I am able to swim, but I can't, because my skin is damaged.
This means that I am capable of swimming, but I am prohibited to do so, because of an infection. So to put it to an explanation:
To be able to talks about an ability to do something, but it does not mean you are allowed to do such.
Can talks about something you are allowed to do, or about your ability to do it. This is therefore ambiguous.
One context where you would have to say “able to” is something like this:
You have to be able to swim every stroke in order to join the swim team.
In this context, “can” isn’t usable. The only other alternative would be:
You have to be capable of swimming every stroke in order to join the swim team.
Stroke = butterfly, back stroke, breast stroke, and freestyle.
I think the question here is not between can and be able to but rather between can and will be able to. As per my knowledge, can says that he is capable of doing it, and it does not say whether he is going to or not, whereas will be able to says that he is going to do it (in the future). You may want to use will be able to if you want to express your willingness to do it.