Question

could have done something 与 should have done something有什么区别？

Answer 1

could have done something 本可能做某事
例: I could have studied in Fudan University if I had done better in College Entrance Exam. 假如我高考考好一点的话，本来有可能在复旦大学念书的。
should have done something 本应该做某事 （该做的没做）
例："You should have handed in your homework this morning." the teacher said angrily. 老师生气地说：“你本应上午交作业的。”

Answer 2

could have done something
本可以做某事（过去）
should have done something
该做某事而未作（也是指过去）

Answer 3

前面一个是：本来可以完成某事
后面一个是：本来应该完成某事