I have a question about the difference between とおり and ように.
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According to "A Dictionary of Intermediate Japanese Grammar", page 517:
In some contexts, ように, the adverb form of ようだ, also expresses the idea "in such a way"(just like とおり).
However, Xように basically means that the way someone does something or something takes place is like X, while Xとおり means that the way someone does something or something takes place is the same as X.
Thus, in contexts where the way is practically the same as X, ように and とおり are almost interchangeable.
先生が言ったように: like the teacher said
先生が言ったとおり: exactly as the teacher said
The difference is small, but ～ように is more akin to "like ～", while ～とおり is "as ～". In your example sentences, the difference may be too subtle. But basically using ～ように allows a small difference from the original, while ～とおり implies something is done exactly in the same way.
For example, 彼が言ったように言う sounds like "to speak/talk like him", while 彼が言ったとおりに言う sounds like you reproduce what he said, word by word.
「先生が言ったように、試験は難しかった」 can be translated as “The exam was difficult as the teacher had told me (predicted it),” and I don’t find any difference from 「先生が言ったとおり、試験は難しかった」.
Both 「通り/とおり」 and 「ように」 mean “as” and “like, and ”are saying the same thing to me.
By the way, when I say this phrase to my English teacher, I would use polite expression, and say 「先生がおっしゃった通り、試験は難しかった(です)」
To me they are interchangeable. However, if I’m forced to tell the difference between “ように” and “とおり,” ”ようにsound a bit softer than ”“とおり、通り” as you see in the following examples. But it could be just a ”気持ちの問題 – a matter of your taste,” as we call.
好きなようにカットしてください- Cut it as you like.
彼女はまるで見てきたように話した – She told as she has seen it.
みんなで決めたように行動しよう – Let’s do as we’ve agreed on.
法の定める通り – according to / abiding with the law.
約束（規則）通り – according to one’s promise.
予想（予定）通り – as planned, per schedule
定刻通り - in an exact time as decided.
計算通り – as calculated, as considered
みんなで決めた通りに行動しよう - Let’s act as per we’ve agreed on.