I think the short answer is "no". There's no single word that captures what you're asking for, i.e. the difference in intensity of nouns describing different points within the spectrum of a specific attribute.
This may well be because many such nouns invoke a highly subjective response; in a fluid language like English, their impact and even their meaning is subject to variation over geography and time and between individuals. This is particularly true of words that can be intended or taken as an insult.
The example you've given - the difference between "idiot" and "fool" - is a case in point. While being described as either is almost certainly insulting, the two words actually address two different attributes, intelligence and wisdom, the gradations of each being highly contestable in their own right without even considering how to weigh the difference between the attributes themselves.
Up to about sixty years ago, "cretin" (severe), "idiot" (severe), "imbecile" (moderate), "moron" (mild) and "feeble-minded" (mild) defined specific levels of intellectual disability. By the 1960s, however, these terms had been replaced by the more generic "mental retardation", and the euphemism treadmill delivered "retard" as the new insult; the latter is still extremely offensive, whereas few nowadays would rely on the historic differentiate between "idiot" and "moron" in judging intensity of insult.
"Fool", on the other hand, describes "A person who acts unwisely or imprudently; a silly person". The attribute here is not intelligence but wisdom - "the quality of having experience, knowledge, and good judgement". Synonyms include clown, goose, sucker, and my favorite pejorative, buffoon.
However, trying to categorise such nouns, whether by intensity or by attribute, is a risky business. Stupidity can refer to a lack of intelligence or wisdom. Amongst the other synonyms of fool, "oaf", "galoot" and "schlemiel" bring with them a sense of clumsiness, "duffer", "wally", "dipstick" and "nincompoop" add a sense of incompetence, "dunce" and "ignoramus" introduce the dimension of education, and "nerd" and "dweeb" the dimension of social ability.
Finally, it would be remiss of me not to mention some antepodean synonyms for idiot or fool: dill, drongo and boofhead. Someone trying to order these synonyms in severity of insult might be a galah.