區別就是兩者都是be angry+介詞短語，不同的介詞引出來的短語意思也不同，具體的不同如下

be angry for中文意思是生氣

Don't be angry for me for long and don't lock me up as punishment.不要對我生太長時間的氣，不要把我鎖起來作為懲罰。

be angry at中文意思是對……發怒

This was their mother at her worst. Her voice was strident, she was ready to be angry at anyone.

1、be angry at+名詞(對...氣憤)；多針對人的言行而言

例句：

I was angry at his careless .

Anybody will be angry at being kept waiting so long.

The teacher was rather angry at what you said.老師對你說的話相當生氣。

The man was angry at being kept waiting.這個人因別人讓他久等而很惱火。

The professor was angry at John for cheating in the exam.教授對約翰考試作弊十分氣惱。

2、be angry for sth 因為某事而生氣。

例如：

I was angry with myself for making such a stupid mistake.

我因為犯了這麼愚蠢的錯誤而在生自己的氣。

He was angry with me for not having done anything.

因為我什麼也沒做，他對我很生氣。

I was angry with him for keeping me waiting.我對他很生氣，因為他讓我等了好久。

He get angry with me for not have write.他因我不給他寫信對我生氣。

I am angry with myself for making such a stupid mistake.我因為犯了這麼愚蠢的錯誤而在生自己的氣。

3、be angry 之後除搭配介詞外，還可接不定式或從句：

（1）He’ll be angry to find that nothing has been done.他發現什麼都沒做，他會生氣的。

（2）I was angry to hear it.我聽了這話而生氣。

（3）He was angry that the door was locked.門鎖上了，他很生氣。

（4）She is angry that he has not answered her letter.他還沒有回信，她生氣了。

（5）We were angry that our request had been rejected.我們的請求遭到拒絕，我們感到很失望。