区别是：这两个词组都表示“顺便访问”的意思，但是后面所接的宾语不一样。
drop in on后面接表示人的名词或代词；
drop in at后面接表示处所的名词或代词。
例句：
drop in on
1、It's improper to drop in on him so casually.
这样冒冒失失去找他可不好。
2、I'm sorry to drop in on you without calling.
很抱歉我没有事先打电话就来冒昧拜访了。
3、Oh! I just drop in on him for a chat.
哦，我只是顺便来和他聊聊天。
drop in at
1、Please drop in at my office when you happen to be free.
如果你碰巧有空的话，请到我的办公室来。
2、If I were you, I would drop in at the department store on my way there this afternoon.
我要是你，今天下午到那里去的路上我会顺路去趟百货商店。
3、Now and then they would drop in at the house and chat with the workers.
他们不时到这屋里来和工人们聊天。