Be able to is possible in all tenses - but "can" is possible only in the present and "could" is possible only in the past for ability. In addition, "can" and "could" have no infinitive form. So we use be able to when we want to use other tenses or the infinitive.

"Can" is used more generally than "able to". It has more uses. "Able to" specifically means, do you possess the ability or the skill to do something? "Can" means, is something possible?