Using Can and Be able to

Examples:

(a) Tom is strong. He can lift that heavy box.
(b) I can play the piano. I've taken lessons for many years.
(c) You can see fish at an aquarium.
(d) That race car can go very fast.

Can usually expresses the idea that something is possible because certain characteristics or conditions exist. Can combines the ideas of possibility and ability.
In (a): It is possible for Tom to lift that box because he is strong.
In (b): It is possible for me to play the piano because I have acquired that ability.
In (c): It is possible to see fish at an aquarium because an aquarium has fish.
In (d): It is possible for that car to go fast because of its special characteristics.

(e) Dogs can bark, but they cannot/can't talk.

Negative form: cannot or can't. (Also possible; but not as common; can not, written as two words.)

COMPARE

(f) I can walk to school. It's not far.
(g) I may walk to school. Or I may take the bus.

In (f): I can walk to school because certain conditions exist.
In (g): I am less than 50% certain that I will walk to school.

COMPARE

(h) I'm not quite ready to go, but you can leave if you're in a hurry. I'll meet you later.
(i) When you finish the test, you may leave.

Can is also used to give permission. In giving permission, can is usually used in informal situations, as in (h); may is usually used in formal situations, as in (i).

COMPARE

(i) Tom can lift that box.
(k) Uncommon: Tom is able to lift that box.
(l) Ann will be able to lift that box.
Bob may be able to lift that box.
Sue should be able to lift that box.
Jim used to be able to lift that box.

The use of be able to in the simple present (am/is/are able to) is uncommon (but possible).
Be able to is more commonly used in combination with other auxiliaries, as in (l).


Cheers!
Naeem