1、时态不同
从时态形式来看，can 只有现在式和过去式(could)，而 be able to 则可根据需要使用多种时态，还可以和一些情态动词连用，或用作动词不定式等非谓语形式。could是can 的过去式。
I haven't been able to sleep recently. 最近我睡不着觉。
He can swim. 他会游泳。
He couldn't be a bad man.他不大可能是坏人。
2、含义不同
用于现在时，can 泛指一般的能力，而 be able to 则主要指具体做某件事的能力。could不表示时态。
He can swim. 他会游泳。
I am able to express my idea in a clear way. 我能清楚地表达自己的想法。
Could I have the television on?你能打开电视吗？
3、表能力时不同
如果要表示"一时的能力"，即"在过去某时有某种能力，并顺利地完成某事"，则要用 was / were able to，而不能用 could。could 表示可能或有能力做。
Though he was sick, he was able to swim across the river. 虽然他病了，但他还是游过了河。
I could pass the examination. 我当时有能力通过考试。（有能力，但实际上不一定做得到）
1、时态不同
从时态形式来看，can 只有现在式和过去式(could)，而 be able to 则可根据需要使用多种时态，还可以和一些情态动词连用，或用作动词不定式等非谓语形式。could是can 的过去式。
I haven't been able to sleep recently. 最近我睡不着觉。
He can swim. 他会游泳。
He couldn't be a bad man.他不大可能是坏人。
2、含义不同
用于现在时，can 泛指一般的能力，而 be able to 则主要指具体做某件事的能力。could不表示时态。
He can swim. 他会游泳。
I am able to express my idea in a clear way. 我能清楚地表达自己的想法。
Could I have the television on?你能打开电视吗？
3、表能力时不同
如果要表示"一时的能力"，即"在过去某时有某种能力，并顺利地完成某事"，则要用 was / were able to，而不能用 could。could 表示可能或有能力做。
Though he was sick, he was able to swim across the river. 虽然他病了，但他还是游过了河。
I could pass the examination. 我当时有能力通过考试。（有能力，但实际上不一定做得到）
can 与be able to在用法上既有相同的一方面, 又有不同的地方,这是应该引起注意的。当它们表示能力的时候，是同义的。如：
He can speak two foreign languages.
He is able to speak two foreign languages.
它们用法上的不同主要体现在以下几方面:
1. can只有两种时态, 即can 和could, 而be able to 有多种时态, 如was/were able to, will/shall be able to, have/has been able to等:
I’ll be able to drive the car in a week.
2．表示过去通过努力终于做成了某事要用be able to，而不能用can。如：
I was able to swim to the bank after the boat turned over.
can 和be able to 都可以表示能力.can泛指一般的能力,而且只有两种形式,即:can, could．be able to 则主要指具体做到了某件事的能力，其形式主要是靠be 发生变化，所以形式比can 多．可以说：I can swim. I am able to swim. 但是不能说：All the people could escape from the big fire in time. 只能说：All the people were able to escape from the fire in time.
3．can能表猜测，be able to不能。can的这种用法主要用于疑问句和否定句。
Somebody is knocking at the door. Who can it be?
It can’t be our teacher who is knocking at the door.
其肯定形式是must be。如:
It must be our teacher who is knocking at the door.
must have done something 表示对现在完成或过去动作的猜测，其否定形式是can’t have done。如:
“His parents must have gone abroad.” “No, I don’t think so. They can’t have gone, for I saw them only this morning.”
要特别注意它们的反意问句形式：
He must be a good teacher，mustn’t /isn’t he？
The students must have gone to bed, haven’t they?
They must have finished their lessons yesterday, didn’t they?
could既可以用肯定形式，又可以用疑问或否定形式。如果用could表示现在“可能”，比can语气更加委婉。如：
If you don’t spend enough time on your studies, you could fail in the final examination.
It could be our teacher who turned off the light last night.
与It must be our teacher. 相比,这句话表示的可能性更小, 因为它表示了两种可能性, 既 “可能是”也可能“不是”，而 must be 只表示了一种猜测。
could have done 这个句型有它的特殊含意，表示“本来可能做到而未做到的事”。如： Our class team could have won the game.
再看以下例句：
He cannot be over praised for what he has done for all of us.
他为我们大家做了这些事, 应该受到大大的表扬。 即 “再怎么表扬也不过分”。
4．can 可以表 “允许”, 与may可以互换, 此时不能用be able to 代替。如：
“Can / May I sit here？” “Yes, please.”
由于may not 有两个意思, 即 “不可能” 和 “不许可”, 因此使用时要特别注意。如：
He may not go home this weekend.
此句既可以表示 He will probably not go home this weekend.也可以表示 I don’t permit him to go home this weekend. 在口语中，表达这两种不同的含义是通过句重音来解决的。如：
He may `not go home this weekend. (I don’t permit him to go home this weekend.)
He `may not go home this weekend. (He will probably not go home this weekend.)
而在书面表达时不可能使用句重音的手段, 所以最好用can’t代替may not来表示 “不可能”：
He can’t go home this weekend.
5. can 是情态动词，只能用作谓语成分，be able to是普通动词短语，既可以作谓语，也可以作非谓语。如：
Being able to speak English fluently, he has no difficulty in communicating with the Americans at the party.
How I long to be able to communicate with the foreigners in fluent English!
6. be able to 后边接动词不定式表示一种实际情况时，其否定形式不是be not able to，而是cannot。如：
Were you able to catch the first bus yesterday morning?
No, I couldn’t.
7. 一般说来, be able to 后边的动词不定式没有被动语态。如:
I’m sure he is able to correct his mistakes in grammar.
不说: *I’m sure his mistakes are able to be corrected by him.
I'm not able to [can't] explain this. 我不能解释这个问题.
He was able to [could] speak French very well. 他的法语讲得很不错.
但是还是有区别的：
(1) 从时态形式来看,can 只有现在式和过去式(could)两种,而 be able to 则可根据需要使用多种时态,还可以和一些情态动词连用,或用作动词不定式等非谓语形式.例如：
I haven't been able to sleep recently. 最近我睡不着觉.
Our baby will be able to walk in a few weeks. 我们的宝宝再过几个星期就能走路了.
You might be able to persuade him. 你也许能够说服他.
I hope to be able to do the work. 我希望能干得了这项工作.
I regret not being able to help her. 我很遗憾未能帮助她.
(2) 用于现在时,can 泛指一般的能力,而 be able to 则主要指具体做某件事的能力.例如：
He can swim. 他会游泳.
I am able to express my idea in a clear way. 我能清楚地表达自己的想法.
(3) 在表示过去的一般能力时,两者没有很大差别.例如：
I could / was able to play the piano when I was young. 我年轻时会弹钢琴.
但如果要表示"一时的能力",即"在过去某时有某种能力,并顺利地完成某事",则要用 was / were able to,而不能用 could.例如：
Though he was sick, he was able to swim across the river. 虽然他病了,但他还是游过了河.
After five hours of climbing, we were able to reach the top of the mountain. 经过5个小时的攀爬,我们终于登上了山顶.
could 表示可能或有能力做,was [were] able to 则表示能够做且确已做到.比较下面两句：
I was able to pass the examination. 我通过了考试.（不仅有能力,而且实际上做到了.相当于I succeeded in passing the examination.）
I could pass the examination. 我当时有能力通过考试.（有能力,但实际上不一定做得到）
could 还可以用来表示更加委婉，客气的表达。例如：
Could you please give me a hand?
你能帮我个忙吗？
祝你开心如意！
只用于现在式和过去式(could)。be able to可以用于各种时态。
They will be able to tell you the news soon. 他很快就能告诉你消息了。
2）只用be able to
a. 位于助动词后。
b. 情态动词后。
c. 表示过去某时刻动作时。
d. 用于句首表示条件。
e. 表示成功地做了某事时，只能用was/were able to， 不能用could。
He was able to flee Europe before the war broke out.
= He managed to flee Europe before the war broke out.
注意：could不表示时态
1）提出委婉的请求，（注意在回答中不可用could）。
--- Could I have the television on?
--- Yes, you can. / No, you can't.
2）在否定，疑问句中表示推测或怀疑。
He couldn't be a bad man.
他不大可能是坏人。