Fallacy - something that is not true based on given evidence.
Misconception - something that is not true based on a person's or group of people's faulty understanding of something
Both of these words are similar, but I feel the word "misconception" describes information that is passed around as common knowledge and most people don't know that it is actually false.
A fallacy, however, seems much stronger and tends to describe something that someone attempts to prove as true, but is unable to do so because their arguments are not sufficient.