Those are not as different as you seem to believe.
> Sort of how a dictionary is used, it is not that the dictionary must be true we understand that it is possible for it to be wrong, it is just that we agree not to contest it in most cases for ease of conversation.
That is not how dictionaries are used. Dictionaries document how language is used in the recent past by a sufficiently large number of people. They are a trailing indicator of how language is used.
If you description was actually accurate, there would be no new slang (e.g. yeet) and words would not change their usage (e.g. "they" is now also a gender neutral singular).
In a sense the power of a dictionary is that you are allowed to use those meanings (indeed they mostly contain positive information and rarely what words do not mean)
> If you description was actually accurate, there would be no new slang (e.g. yeet)
Completeness ad accuracy are different.
> words would not change their usage (e.g. "they" is now also a gender neutral singular)
Speech can be sometimes accurate and sometimes less accurate. As a medium the value of speech is what you can express with it, it is in general not a form of art per se.
>> In one case I am declaring that something needs to be true, in the other I am declaring that I believe something as true.
>Those are not as different as you seem to believe.
I indeed believe they are quite different, 2=2 must be true in terms of the statements I understand it to be. Evolution on the other hand is something that I simply believe.
I cannot even fathom[1] what a proof of "not 2=2" could be, as in even if you had one I would be unable to understand it or believe it.
Evolution is something that instead can be disproven, even more than that a huge chunk of why scientist believe it is because experimental result could disprove it but instead keep confirming it.
[1] this is an important logical concept: for a statement of facts to be (at the very least) well formed you must be able to understand what it would be required for a proof and/or a confutation.