fame the state of being known about by a lot of people because of your achievements 属于比较大的社会名望
是指一个人红了。。出名了。。成名了，名声大震了。是famous的名词形式。
有点贬义。。
比如：
She won her overnight fame by her first novel.
她的第一部小说一问世，便使她一举成名。
She has always been desirous of fame.
她一直想成名。
reputation the opinion that people have about someone or something because of what has happened in the past 属于个人的名誉，别人对你的看法，比较小。
好的名声，名气，名誉，威望的意思。。。一般是褒义的。
比如：
This store has an excellent reputation for fair dealing.
这家商店因公平交易而获好名声。