当它们表示能力的时候，是一样的。
其区别如下：
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。
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。
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。
4．can 可以表 “允许”, 与may可以互换, 此时不能用be able to 代替。
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
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。
7. 一般说来, be able to 后边的动词不定式没有被动语态。
can
1、Pork is also the most versatile of meats. It can be roasted whole or in pieces.
在肉类中，猪肉的做法也是最多的，可以整块烤来吃，也可以切片烤来吃。
2、Don't worry yourself about me, I can take care of myself.
你别担心我，我能照顾好自己。
3、People who can't afford to go to the theatre or concerts can afford to go to football matches.
看不起电影或听不起音乐会的人可以去观看足球赛。
4、A vacant lot or a bombsite can, to the amateur naturalist, produce an extraordinary variety of flora and fauna.
对于业余博物学者来说，在一片空地上或被炸后的废墟里可能发现种类繁多的植物群和动物群。
5、From her knowledge of Douglas's habits, she feels sure that the attacker can't have been Douglas.
根据她对道格拉斯习性的了解，她敢断定他不可能是那个袭击者。
be able to
1、They may be able to help with childcare so that you can have a break.
他们可以帮忙照料孩子，这样你就可以歇一歇了。
2、If only I could get some sleep, I would be able to cope.
要是能睡上一会儿，我就能应付了。
3、If you need help at work, your Personnel Manager should be able to help.
如果你工作中需要帮助，人事经理应该能帮上忙。
4、It must be better to be able to offer them love and security.
要是能给予他们关爱和安全感肯定会更好。
5、Without them you will not be able to fulfil the tasks you have before you.
没有他们你将无法完成面临的任务。