How to distinguish between different values of a hyperparameter in communication?
TLDR: Basically, you have answered your question with your quote from Wikipedia: the common terminology is &quot;values&quot;.

The question on SE SO which you have quoted discusses the terminology from a software development perspective. But there is a difference between the use of the word &quot;parameter&quot; in software development and machine learning. This is how Wikipedia defines parameter from a software development perspective:

In computer programming, a parameter or a formal argument, is a special kind of variable, used in a subroutine to refer to one of the pieces of data provided as input to the subroutine. These pieces of data are the values of the arguments (often called actual arguments or actual parameters) with which the subroutine is going to be called/invoked. An ordered list of parameters is usually included in the definition of a subroutine, so that, each time the subroutine is called, its arguments for that call are evaluated, and the resulting values can be assigned to the corresponding parameters.

Let's make an example:
n_estimators = 100
model = RandomForestRegressor(n_estimators=n_estimators)

From a software development perspective n_estimators is a parameter, 100 is the parameter's value and n_estimators=n_estimators is the argument.
Howevever, in machine learning terminology you'd consider n_estimators a hyperparameter and 100 its value. Going back to your examples I would just do something like this:
hyperparameter_dict = {
    &quot;learning_rate&quot;: 0.001,
    &quot;dropout&quot;: 0.25,
}

and
for hyperparameter, value in hyperparameter_dict.items():
    ...


Introducing a new terminology which is not common in machine learning (like &quot;hyperarguments&quot;) would only cause confusion and not make your code or communication any clearer.