都有区别。
1、can have done 和could have done 的区别
can have done是表示应该做某事而没有做,所以既然知道没有做,那肯定是已经发生了。
could have done 表示本能做而实际未做,是虚拟语气.
2、can't have done和couldn't have done的区别
can't have done（不可能做过）是must have done（一定做过）的否定形式.
couldn't have done(可能没做过)是may have done(有可能做过)的否定形式.
一般认为can't have done有80%以上的把握。而couldn't have done则委婉的多，只有50%左右的把握。
拓展资料：
He would not die If I could have helped him。
如果当时我能帮助他,他就不会死。
He could not have gone anywhere,I just saw him.
他不可能去哪里的,我刚刚都还看见他.
Mr. Smith can't have gone to Beijing, for I saw him in the library just now。
史密斯先生不可能去北京了，我刚才还在图书馆见过他。
参考资料：
动词 + 动词完成式即“情态动词 + have + done”，表示对过去行为或动作进行推测、评论或判断。这个结构是近几年高考情态动词的重点和难点。
一、在虚拟语气中的用法
1. should have done 表示“过去本应该做某事却未做。”其否定结构 shouldn't have done 表示 “过去本不该做某事却做了。”
2. ought to have done 表示“过去本应该做某事却未做。”其否定结构 oughtn't to have done 表示 “过去本不该做某事却做了。”
3. need have done 表示“过去本有必要做某事却未做。”其否定结构 needn't have done 表示 “过去本没必要做某事却做了。”
4. could (不能用 can) have done 表示“过去本能够做某事却未做。”注意：其否定形式 couldn't have done 没有虚拟语气的用法，couldn't have done 只能表推测，相当于 can't have done，意为：“过去不可能做了某事。”
5. might (不能用 may) have done 表示“过去本可以做某事却未做。” 注意：其否定形式 might not have done 没有虚拟语气的用法，might not have done 只能表推测，相当于 may not have done，意为：“过去可能没有做某事。”
二、表推测的用法
1. must have done
表示对过去某事的肯定猜测，译为：过去肯定做了某事。不存在 mustn't have done 的形式。其否定或疑问形式须用 can(could) 来表示. 例如：
Since the road is wet, it must have rained last night. 既然路是湿的，那昨天晚上肯定下雨了。
He can't have missed the way. I drew him a map. 他不可能迷路。我（当时）给他画了张图。
“The dictionary has disappeared. Who could have taken it?” 词典不见了，（过去）谁可能把它拿走了？
2. may / might have done
may / might have done 表示“过去可能做了某事”。may 比 might 表示的可能性在说话人看来稍大些。may/might not have done表示“过去可能没有做某事。”例如：
I can't find my keys. I may / might have left them at the school yesterday. 我找不到我的钥匙了。我可能昨天把他们落在学校了。
John may/might not have passed the exam; he looks very sad.约翰可能没有通过考试。他看起来很忧伤。
注意：may/might have done表推测不能用于疑问句中。
3. can/could have done 表推测一般用在否定句和疑问句中，表示不相信或怀疑的态度。
Can/Could he have passed the exam?他可能通过了考试吗？
I think that he couldn’t/can't have gone abroad. I saw him just now.我认为他不可能出国了。我刚才还看见他了。
注：表示推测过去某动作发生的可能性时，就表示的可能性程度而言，must 最大，could 其次，may 更次之，might 最小。例如：
“I wonder how Tom knew about your past.” “我想知道汤姆是怎么知道你的过去的。”
“He must / could / may / might have heard of it from Mary.” “他肯定/很可能/可能/兴许（没准儿）已从玛丽那儿听说此事了。”
三、高考例析
1. Sorry I'm late. I ________ have turned off the alarm clock and gone back to sleep again. （2000 北京春季）
A. might B. should C. can D. will
答案为 A。表推测的用法。句意：对不起，我迟到了。我（当时）兴许是关了闹钟又回去睡觉了。might 相当于 may, 但语气更加不肯定。
2. I was really anxious about you. You_________ home without a word. （01 全国）
A. mustn't leave B. shouldn't have left C. couldn't have left D. needn't leave
答案为 B。虚拟语气用法。句意：我（那时）真地很担心你。你本不应该不留个话就离开家。
3. — I’ll tell Mary about her new job tomorrow.
— You________ her last week. （04 福建）
A．ought to tell B．would have told C．must tell D．should have told
答案为 D。虚拟语气用法。句意：---我明天要告诉她我的新工作的情况。 ---你本应该上周告诉她。
4. — Tom graduated from college at a very young age.
— Oh, he ______ have been a very smart boy then. （04 全国IV）
A. could B. should C. might D. must
答案为 D。表推测的用法。句意：——汤姆很年轻的时候就大学毕业了。——哦，他肯定是一个很聪明的男孩儿。
5. He _______ have completed his work; otherwise, he wouldn't be enjoying himself by the seaside. (05 北京卷)
A. should B. must C. wouldn't D. can't
答案为 B。用法同4题。句意：他肯定做完了工作，不然他就不会在海边痛快地玩儿了。
6. — Do you know where David is? I couldn't find him anywhere.
— Well. He have gone far—his coat's still here. （05湖北卷）
A．shouldn't B．mustn't C．can't D．wouldn't
答案为 C。表推测的用法。句意：—你知道大卫在哪儿吗？我哪儿也找不到他。—瞧，他不可能走远—他的上衣还在这儿呢。can't 相当与 couldn't，但后者语气更加委婉。
四、练习
1. — The woman biologist stayed in Africa studying wild animals for 13 years before she returned.
— Oh, dear! She _______ a lot of difficulties! (05 江苏卷)
A. may go through B. might go through
C. ought to have gone through D. must have gone through
2. I have lost one of my gloves. I ________ it somewhere. （05 北京春季）
A. must drop B. must have dropped
C. must be dropping D. must have been dropped
3. Mr. White _____ at 8:30 for the meeting, but he didn't show up. （04 广西）
A. should have arrived B. should arrive
C. should have had arrived D. should be arriving
4. He paid for a seat, when he ______ have entered free. （05 山东卷）
A. could B. would C. must D. need
5. — Tom is never late for work. Why is he absent today?
— Something ________ to him. (05 江西卷)
A．must happen B．should have happened
C．could have happened D．must have happened
6. I _______ have been more than six years old when the accident happened. （05 天津卷）
A. shouldn't B. couldn't C. mustn't D. needn't
7. This cake is very sweet. You __________ a lot of sugar in it. （05 辽宁卷）
A．should put B．could have put C．might put D．must have put
Key: D B A A D B D
can have done和could have done有区别。
can't have done和couldn't have done有区别。
1.can+have+done表示对过去行为的怀疑,用于疑问句,译成“可能做过……吗?“
2.could+have+done是虚拟语气,表示对过去事情的假设,意思是本来能够做某事而没有做。
3.could (不能用 can) have done “表示“过去本能够做某事却未做。”注意：其否定形式 couldn't have done 没有虚拟语气的用法。
4.couldn't have done 只能表推测,相当于 can't have done,意为：“过去不可能做了某事。”
拓展资料：
can have done、could have done、can't have done、couldn't have done的例句：
1.Can she have done her homework?
她可能做完家庭作业了吗？
2.Yes, perhaps I could have done better, but that's not what I want in life.
是的或许我可以做得更好，但这是不是我要的生活。
3."She can't have done anything so stupid," she cried in distraction.
“她这么做再愚蠢不过！”她心烦意乱地嚷道。
4.I couldn't have done any of this without Beatrice and mullet fingers.
没有比阿特丽斯和红鲻我也做不到这些。
could have done 本来可以完成
cant 不能
couldn't 不能过去式
