When somebody uses 声が出る, what is the significance of saying it this way as opposed to using 言う? Is this used commonly and does it have some sort of special nuance I'm not aware of?
When you use "say" or "言う", the content of the speech is the most important. The existence of the physical sound/voice is not usually important, nor necessary.
- Dictionaries say so.
On the other hand, when we use "声が出る" (intransitive) or "声を出す" (transitive), the existence of the physical sound is the most important concern. The content (what is said as a word) is not very important. For example, you cannot use "言う" in the following sentences:
- (in a quiet classroom) 驚きのあまり、声が出てしまった。
- 病気が治って、また声が出るようになった。(or 声を出せるようになった)。
- (watching music video) 3人の中で、彼女が一番声が出ている。
- (while sneaking) シッ！ 大きな声を出すな！ (≒ keep your voice down!)
If the physical voice and the content is both important to you, you can also use "声に出して言う" (say out loud).
- (to kids) 間違ったら、「ごめんなさい」と声に出して言いなさい。
It is different to the translatation of "声に出る" in English, because English does not have such expressions. An expression like "声がでる" is called "自発表現" in Japanese.
This expression means: Something makes a person do naturally. If I must translate "声が出る" into English, it would be I was naturally made to say.