区别就是两者词性是不一样，具体的不同如下
over表结束了是形容词
finish是动词，但be over=finish，中文意思是结束，完成了。
例如
Our budding romance was over.我们刚刚萌发的浪漫爱情结束了。
=Our budding romance finished
我们到达时，会议已经结束了。By the time we arrived the meeting was over.
怎么区别over和finish
over 与finish（结束……）
over作此意讲一般是副词，前面必须有动词才能做谓语，一般结构是be over. 例如：School is over， I went straight home.
而finish是动词，后面接名词或动词的ing形式。例如：
I finished my homework， I went to bed.
或I finished doing my homework， I went to bed.
