I just stumbled across a new phrase 无消息。
This is the first time I've encountered 无.
How it is used, and how it is different from 没有，as in 没有消息？
It is hard to give a rule on using 无 vs 没有， even they mean the same.
Only 无 is used:
无所谓 （We don't say 没有所谓, but some people say 没所谓）
无线电 （We don't say 没有线电）
无论如何 （We don't say 没有论如何）
无性繁殖 （We don't say 没有性繁殖）
Only 没有 is used:
我没有钱 （We don't say 我无钱）
你没有失败 （We don't say 你无失败）
Both can be used:
没有 消息就是好消息。 or 无 消息就是好消息。
没有 人能猜出这个谜语。 or 无 人能猜出这个谜语。
I think there are still some clues on using 无 vs 没有.
沒有 is the common word for "no/none" used in conversation.
無 is a character that is used in words and set phrases, and cannot be used by itself.
Put it in simple way,
无 means lack of (noun objects), i.e. 无语（lack of speech-> speechless）
没 means lack of (an action), i.e. 没有（lack of having-> don't have）
So it would be better to compare 无 and 没
In general, the meaning of "无" is "沒有".
"沒有", can serve as a component of a sentence. I think in technical terms, you can say it can serve as predicates in sentences.
So in this sense, "没有" is more like "There be no" in a sentence. For example:
Technically, "无" is more similar to "no","non-", "-less", "-free" in English when constructing a phrase or word. It sounds more formal, and it normally (in modern Chinese) cannot be used as predicates in sentences.
basically, same meaning, but 没有 for modern people, 无 for people from hundred years ago....
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In my opinion, the most significant difference is that 无 can be used as a bound morpheme, but 沒有 is always a word.
For example 无形资产 can never be "沒有形资产". It is 无形的, and it 沒有实物形态.