He doesn’t dare to say anything.
Is the English translation accurate? I would expect “Er wagt es nicht, etwas zu sagen”. The German sentence looks like “He doesn’t trust himself to say anything”, which doesn’t feel like it has the same meaning to me.
It is okay.
“sich nicht trauen” = to not dare"
“sich (selbst) nicht vertrauen” = “to not trust yourself”
Surely the same root, but different meanings.
I tend to use the Wiktionary popover a lot these days, and the Wiktionary page for trauen says as one of the definitions -
[3] (reflexive, with zu + infinitive) to dare (to do something)
I often then use my browser to check on the original language page, and there The German Wiktionary page for trauen has a definition -
[2] reflexiv: etwas wagen
Thanks guys. I had “trauen” and “vertrauen” mixed up in my head, and I wasn’t familiar with “sich trauen” meaning “to dare”. You learn something every day!
“trauen” and “vertrauen” are not so different. So it’s not surprising to get them mixed up. It’s only the reflexive version of “trauen” that also has a different meaning:
sich (acc) trauen - to dare
sich (dat) trauen - to trust oneself
sich (dat) vertrauen - to trust oneself
Ich traue mich - I dare
Ich traue mir - I trust myself
Ich vertraue mir - I trust myself
So it’s only with “sich” that it becomes ambiguous, because “sich” is the same for dative and accusative. But then, it’s uncommon to say that you trust yourself, so the default interpretation is “to dare” (when it’s not unambiguous because you can tell the case from the pronoun).
But I actually think the “different meaning” is not so different after all. I’d say if you substitute “to trust” with “to have faith”, you can see that it’s not that big of a step: I trust myself → I have faith in myself → I dare.
Now, for the difference between “trauen” and “vertrauen”… It’s actually not so easy.
I’d say “trauen” is more situational, immediate, and concerning one single thing. For example you trust that some statement is true, of if you don’t trust, you suspect a scam, etc. You can trust that a layer of ice holds your weight. There’s a phrase “Ich traue dem Frieden nicht”, which basically means “something’s fishy”.
“vertrauen” is more general and long-term. It expresses familiarity, and means you are willing to give up control, your money, your life, etc. and put them into the hands of the one you trust. Which also means it is usually only used with people, because you believe in their good intentions, which inanimate objects don’t have.
For example:
Ich traue dem Eis. (It will hold my weight and not break)
Ich vertraue dem Eis. (sounds weird, unless you want to anthropomorphize the ice)
Ich vertraue darauf, dass das Eis hält. (but this works 
)
I think english makes a similar distinction with “to trust” vs. “to trust in”?
Now you’re making me think about my own language 
“I place my trust in the ice, not to break” → this sounds odd to me, and is something I don’t think many people would say, but it might work.
“I trust the ice not to break” or “I trust that the ice won’t break” are both fine.
In reference to people, either way works:
I place my trust in you = I trust you
I like your comparison to “faith”, because that also works:
I have faith that the ice won’t break → this works
I have faith in the ice, not to break → This sounds odd to me, but might work.
On the topic of “sich trauen” vs. “wagen”.
Both can be translated with “to dare”, but “wagen” can also mean “to have the impudence”, while “sich trauen” is strictly “to have faith in oneself” or “not be scared to do”.
The typical phrase is “Wie kannst du es wagen? (mich zu beleidigen)”
@Lernen_und_Fahren Well, I was thinking of meaning #2 on wiktionary:
Edit: … although I think that corresponds to “vertrauen auf”:
Ich vertraue Gott. - I trust God.
Ich vertraue auf Gott. - I trust in God. (= I trust that he will help me when I’m in need)