Given America's English common law heritage, precedents are vital in understanding the basis of past and present judicial decisions, which can sometimes "stand" for hundreds of years, with only minor modifications.
In theory, the essence of "a rule of law" is static, but it must be applied dynamically on a case-by-case basis, since each case is unique and must be treated as such. That is why the notion of distinguishing features is so important in arguing the merits of a case, whether you are a lawyer for the defense or for the plaintiff.
For example, the terrorist attack in New York City on 9/11 (2001) and the Boston Marathon bombings in 2013 have this in common: both were criminal acts. You could perhaps find and label many other similarities or analogs between the two events. By the same token you could also find and label some distinguishing characteristics.
Let's for illustrative purposes call the two incidents "New York City" and "Boston." One legal expert in analyzing them might say, "I distinguish New York City as a carefully and skillfully executed plan of the international terrorist group Al-Qaeda." Another legal expert might say, "I distinguish Boston as a clumsily executed plan of two disaffected outsiders with only the loosest connections to an international terrorist group."
And so it goes within the halls of justice as lawyers look for analogous and dis-analogous facts and factors in order to determine how well a given rule of law "fits" or does not fit a given case. Dis-analogous--or distinguishing--factors, and analogous--or similar--factors are compared and contrasted to determine how well or poorly the facts of the case at hand can be guided by the rule of law as it now exists after having evolved (if only incrementally) and been applied to perhaps scores of cases in the past.
One lawyer might argue that the "Libbey" case from 1997 is distinguished from the "Hanover" case he is currently arguing in 2013 in that there was no mastermind in Libbey, but only a rag-tag bunch of radicals with no connection to any other radical groups, whereas in Hanover there was clearly a mastermind who planned and implemented the crime with the help of a well-trained and disciplined group of ex-military personnel. Based on the distinguishing facts at hand, then, the lawyer for the defense argues that the rule of law does not apply to Hanover in the same way it did to Libbey. He then says, "I rest my case."
The lawyer for the plaintiff, however, argues there is another analogous and overriding factor making Libbey relevant to the case at hand, and therefore the rule of law as it applied to Libbey also applies to Hanover. She then says, "I rest my case."
Distinguishing facts and analogous facts, they all are used in arguing the merits of a given perspective on a given case. Which facts prove ultimately to be more persuasive and controlling depends largely on judges and juries and their fallible interpretations of how the law should be applied to the facts at hand. Thankfully, sometimes the truth manages to emerge from such deliberations!