连接代词包括who, whom, whose, what, which, whoever, whomever, whichever, whatever，用于引导从句或不定式。
连接副词可分为两类，一类是用于连接句子或从句，常见的有therefore, besides, otherwise, however, moreover, still, thus, meanwhile等；另一类是用于引导从句或不定式，主要的有when, why, where, how 等。
连接代词/副词除了具有连接从句或不定式的作用外，在从句和不定式中也充当句子成分，如宾语、状语。其中宾语是名词性成分，用连接代词实现，而状语是副词性成分，用连接副词实现。
可用于引导不定式的连接代词：who, whom, whose, what, which
举例：
I asked him what to say next. = I asked him what I could say next. 我问他接下来我该说些什么。(what在宾语从句和不定式中作宾语)
Show me what to do. = Show me what I should do. 给我说说该做什么。(what在宾语从句和不定式中作宾语)
Did you ask her which to do first? = Did you ask her which you should do first? 你问没问她该先做哪一个? (which在宾语从句和不定式中作宾语)
He doesn’t know whom to believe. = He doesn't know whom he should believe. 他不知该相信谁。(whom在宾语从句和不定式中作宾语)
I wonder who to date. =I wonder who I should date. 我拿不定该跟谁约会。(who在宾语从句和不定式中作宾语)
I've forgotten which path to follow. = I've forgotten which path I followed. 我已经忘记我沿着哪条路来的。
这类用法通常可视为名词性从句的省略。这就是如你所说的"在动词tell, advise, show, teach, find out, decide, discuss, forget等后，常用一个带连接代词/副词的不定式作宾语。"的情形。
可用于引导不定式的连接副词：when, why, where, how
举例：
When to stop swaddling their baby is a big question for all new parents. = For all new parents, when they can stop waddling their baby is a big question. 对所有初为人父母者来说，什么时候开始停止襁褓包裹婴儿是一个大问题。(when在主语从句和不定式中做时间状语)
I couldn't see the reasons why to do so. = I couldn't see the reasons why you/we do so. 我不知道这样做的理由是什么。(why在定语从句和不定式中做原因状语)
First,we have to decide where to live. = First, we have to decide where we will live. 首先我们得确定在哪儿住下来。(where在宾语从句和不定式中做地点状语)
I'm not sure how to tell the difference between them. = I'm not sure how I can tell the difference between them. 我不确定它们之间的区别。(how在宾语从句和不定式中做方式状语)
回到你的句子：We must decide whether to go or stay. = We must decide whether/if we should go or stay. 我们得决定去还是留。(连接词whether在从句中不充当句子成分，只起连接作用)。此时在不定式中不能用if连接。
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