maxim
a well-known phrase that expresses sth that is usually true or that people think is a rule for sensible behaviour
e.g. I believe in the maxim 'if it ain't broke, don't fix it'.
motto
a short sentence or phrase that expresses the aims and beliefs of a person, a group, an institution, etc. and is used as a rule of behaviour
e.g. Our motto is 'Plan for the worst and hope for the best'.
dictum
a statement that expresses sth that people believe is always true or should be followed
e.g. ...the dictum that it is preferable to be roughly right than precisely wrong...
wisdom
You can use wisdom to refer to ideas that are accepted by a large number of people.
e.g. Health education wisdom in the UK differs from that of the United States...
witticism
a clever and amusing remark
adage
a well-known phrase expressing a general truth about people or the world
e.g. ...the old adage, 'Every baby brings its own love'.
What's the difference between maxim and adage?
In short, they're probably all different, but the difference is quite nuanced. So, unfortunately, I can't really answer the question[1] .
My understanding is that "maximum" seems to be more modern, while "age" is more ancient.
The word "adage " may not be so commonly used. We use "proverb" more. (Adage: synonym with proverb).
So, how to translate "格言" and "名言" into English?
We can remove "wisdom" and "witticism". The remaining four words "maxim", "motto", "dictum" and "adage" have similar meanings, but they have differences.
According to the analysis just now, "adage" is more inclined to the "old proverb", so it should also be removed.
Now, the words left are:
"maxim", "motto", "dictum"
What's the difference between Dictum and Motto?
- Dictum: An authoritative declaration.
- Motto: A favorite saying of a sect or political group[2].
"motto" is usually pretty old, and kind of like the founding principle of an establishment[3]?
e.g.
- Motto: Mortui viventes docent
- Maxim: bad cases make bad law
- Idiom: it's raining cats and dogs.
You see that Motto is written directly in Latin.
Maxim is like telling you a rule in the world.
Idiom looks like a shorthand for certain things.
So "maxim" should be the most suitable word to translate as "格言". Because it also represents a certain sentence that people firmly believe.
If "名言" is directly translated, it should be "famous word" or "famous sentence"or "Famous sayings".
Famous sayings generally refer to words spoken by famous people.
The reason why I say this is because I found it seems like "motto", which can be a synonym.
References:
[1] https://hinative.com/en-US/questions/16018928