Folksonomy and Ontology lie on two opposite ends of the same divide.
A Folksonomy is built to aid navigation and subjective interpretation. Folksonomies categorize A as a B because it is interesting for users to also consider A when seeing B. As an Example: Awards -> Television. An award is of course not a television, this connection is purely to aid navigation.
An Ontology is built to provide objective meaning, ontologies categorize A as a B because, in meaning, A is a specific subtype (subclass) of B. As an Example: Television Award -> Award. Or wine -> Potable Liquid.