False Equivalence is a logical fallacy where there appears to be a logical equivalence (usually in quantity and quality of evidence) between two opposing arguments, but when in fact there is one side has substantially higher quality and quantity of evidence.
However, there is no equivalence between the two sides when one is supported by evidence, and the other side with little or no evidence, of which most is of low quality. In other words, in false equivalence, someone will state that the opposing arguments have a passing similarity in support, when, on close examination, there is a large difference between the quality of evidence.
A False Balance is a form of false equivalence. Journalists use false balance when comparing two sides of a story (especially in science) by making it appear that both sides of the “debate” have equivalent authority and evidence supporting it. However, if one “side” has more evidence supporting it than the other, but the journalist fails to give proper weight to the evidence-based side, then it is trying to present false balance.