In Matlab R2022a:

>> nchoosek (100, 50)
Warning: Result may not be exact. Coefficient has a maximum relative error of 1.6875e-14, corresponding to absolute error 1702580784238102.
> In nchoosek (line 121)

ans =

   1.0089e+29

>> lastwarn

ans =

    'Result may not be exact. Coefficient has a maximum relative error of 1.6875e-14, corresponding to absolute error 1702580784238102.'

>> lastwarn('test')
>> lastwarn

ans =

    'test'

>> warning off;
>> nchoosek (100, 50)

ans =

   1.0089e+29

>> lastwarn

ans =

    'Result may not be exact. Coefficient has a maximum relative error of 1.6875e-14, corresponding to absolute error 1702580784238102.'

>> lastwarn('test')
>> warning on quiet
Error using warning
Unknown setting or incorrect message identifier 'quiet'.

So, it looks like `warning off` in Matlab behaves like `warning on quiet` in Octave.
Matlab doesn't understand `warning on quiet`.

Here is a demo with Octave 8. Default behavior:

$ octave -f --eval "nchoosek (100, 50), lastwarn"
warning: nchoosek: possible loss of precision
warning: called from
    nchoosek at line 150 column 7

ans = 1.0089e+29
ans = nchoosek: possible loss of precision

Warning off silences lastwarn also:

$ octave -f --eval "warning off; nchoosek (100, 50), lastwarn"
ans = 1.0089e+29
ans =

Warning on quiet silences display but allows lastwarn:

$ octave -f --eval "warning on quiet; nchoosek (100, 50), lastwarn"
ans = 1.0089e+29
ans = nchoosek: possible loss of precision

It's useful because of that difference if the user wants to do fine-grained warning message control, but is not fully Matlab-compatible. Since Octave is generally a superset of Matlab, it's probably better to retain it and document it.

looking at the code for warning, it does appear that there is an undocumented "quiet" warning state. 

the state can be set on/off with the command style call to warning mentioned in comment #0, or by the function style syntax

>> warning("on", "quiet")
>> warning("off", "quiet")

and can be queried like any other warning state by

>> warning("query", "quiet")
"quiet" warning state is "on"

I don't know if this was added for matlab compatibility, as a quick search doesn't turn up anything there. We don't always document things that are added just for that reason. but it would be good to know what this state actually changes and to document it if it's useful.

updating report title and changing to "Need info" from someone more for familiar with the warning function.