1、 be able to 强调通过努力而获得的能力,而can则强调自身已具有的能力.如：
She can sing the song in English.她能用英语唱这首歌.
He will be able to sing this song in English in a few minutes,too.几小时之后,他也能用英语唱这首歌.
2、 be able to 强调一种结果,而can只强调一种可能.如：
Luckily,he was able to escape from the big fire in the end.幸运的是,他终于逃出了大火.
If he got here a few hours earlier,I could save him.要是他早几小时来,我还能救他.
3、 be able to 可以有各种时态；而can只有一般现在和一般过去两种时态.如：
I could help you last night,but you didn't come.昨天晚上我能帮你,而你又没来.
Can you see it there?你能看见它在那儿吗?
He is / was / will be able to help you.他能帮你的忙
Will you be able to camera the lecture tomorrow?你明天能把讲座录下来吗?
I'm sorry I haven't been able to answer your letter in time.真对不起我没能及时给你回信.
Ps:指过去某时或某个时刻设法做成某事,不用could,而用was\were able to.
I talked with her for a long time,and eventually I was able to make her believe me.我谈了很久,最终还是使她相信了我的话.
4、 can可用于表示可能性,推测,允许等情况,而be able to通常不这样用.
You are able to use my pen.(误)
You can use my pen.(正)
5、 can有被动语态,主语为人或物皆可,而be able to只接不定式的主动形式,不接表示被动的不定式,也不可用无生命的名词作主语.例如：
The work is able to be done by him.（误）
He is able to do the work.（正）