In which contexts the usage vary?
closed as general reference by RegDwigнt♦ Jul 1 '12 at 14:12
This question is too basic; it can be definitively and permanently answered by a single link to a standard internet reference source designed specifically to find that type of information. If this question can be reworded to fit the rules in the help center, please edit the question.
Though they both imply there is some kind of mistake, they are pretty different kinds of mistakes.
A fallacy is a common misconception. A logical fallacy is one type of example.
Misnomer refers, more specifically, to a wrong name or inappropriate designation -- for instance, calling Native Americans "Indians."
An easy way to remember the difference is to remember that misnomer is derived from the the Latin word for "name," nominare.
I think Wikipedia has one of the better succinct definitions: "...a fallacy is incorrect reasoning in argumentation resulting in a misconception." It should be noted that there are a number of distinct logical fallacies, and that an entire section of philosophy is devoted to them. The referenced link is a good start for exploring the various flavors of fallacies.
@Mitch's answer to a misnomer is well stated.
A fallacy has a technical and a common usage, but both could be loosely summarized as "an error in reasoning" or a "logical fault".
Poor reasoning can also be called fallacious reasoning.
"Begging the question" is an example of a fallacy. From nobelief's fallacy list:
Here's an example usage from a comment on Serendipity: Or, What has Software Engineering got to do with Climate Change?
Something being a 'fallacy' tends to indicate an error of process.
A misnomer is simply misnaming something, or calling something by the wrong name or a misleading name.
This can be minute and technical or broad and ideological or philosophical:
It is incorrect to use misnomer to mean an incorrect assumption, poor reasoning, or more general kind of error where another word should be used instead:
Don't use it this way, please:
Ugh. From the another comment found in the wilds of the Internet:
Again, please, no: