no matter what：不能引导主语从句，只能引导让步状语从句。
whatever：既可以引导名词性从句，也可以引导让步状语从句，引导让步状语从句时，可以替换为no matter what；名词性从句则不能与之直接替换。
no matter what只能放在句首，在句中，只能用whatever 。“no matter +疑问词" 或"疑问词+后缀ever" 。
引导状语从句例句：
No matter what happened,he would not mind.=Whatever happened,he would not mind.
引导名词性从句例句：
No matter what you say is of no importance now.(错)
Whatever you say is of no importance now.(对)
第一句的no matter what you say 这一部分是整句句子的主语，所以no matter what 引导的是主语从句，但是no matter what 是不能引导主语从句的（名词性从句的一种）,所以这句话是错的。
而第二句的whatever you say 也同样是句子的主语，而whatever 可以引导名词性从句,所以这句话是对的。
拓展资料：
no matter how 与 however 的用法
1、however可以做副词,含义为“但是,可是,不过”.多插在句中,有时放在句首或句尾.
例如：However,they did not seem to have much effect.
不过,他们似乎没有起太大的作用.
He said that it was so;he was mistaken,however.
他说事情就是这样；然而,他错了.
由上文可以看出,第五单元的文章中的三句话中,however做副词,同学们可以试着翻译一下.
2、however还可以做连词,含义为“不管……如何,多么”,引导让步状语从句.从句的语序为：however+adj./adv.+主语+句子的其他成分.
例如：We shall never succeed,however much we try.
无论我们多么的努力,都不可能成功.
However cold it is,she always goes swimming.
无论天多冷,她总是去游泳.
注意：当however做连词时,可以转换为no matter how,因此上面的两个例句可以转换为：
We shall never succeed,no matter how much wetry.
No matter how cold it is,she always goes swimming.
从构词法的角度看,词尾加-ever的常用词还有：whoever,whomever,whosever,whatever,whichever,whenever,wherever等,这些词都可以引导让步状语从句,而且当它们引导让步状语从句时,可以转换为no matter who(what,when,where,which….).nomatter…是连词词组,做“不管”,“无论”解,no matter what(when,where,who)等的含义为“不管什么(何时,哪里,谁)”
例如：No matter who(=Whoever) knocks,don’t open the door.
不管是谁敲门,都不要开.
No matter what (=Whatever) happened,he would not say a word.
不管发生什么事,他总是一言不发.
I go to the theatre no matter when(=whenever) I get the chance.
每当我有机会,我就到剧院去.
No matter where(=Wherever) you work,you must write to me.
无论你在何处工作,一定要给我写信.
No matter whether you have time or not,you must deliver these clothes today.
不管你明天是否有时间,你必须今天把这些衣服送去.