The lexicographers might step up, please.
The degrees you are looking for is the description of the definitions of words as their usage is enumerated in the dictionary. As you move from definition 1 to 5 and onward you will see the most common usage first and increasingly less common usages later. This is apparently not done in Merriam Webster
Usages primarily concern themselves with their audience. Advertisers use "chemical" to get a negative reaction from the majority of people. They even say it with a tone to show that it is not pleasant. Away from sales pitches a discussion about chemicals need have no negative interpretation.
"Theory" is a great example. Anyone defending the theory of Evolution is always pointing out that a proper theory is not described in the top two usages in the dictionary. There you see a theory as a general possibility not a scientific hypothesis.
Your degrees of precision are precisely those set forth ad seriatim in each definition. The name for such a listing out I cannot provide.