Groundwork

First up some basic definitions
  • Tagsonomy - This is a set of tagged resources, each resource has one or more "tags" which are not limited to any preset vocabulary. 
  • Folksonomy - A collective tagsonomy, usually the aggregate of a group of users personal tagsonomies.
  • Tag Map - The structure used to represent a tagsonomy.
  • Weighted Tag Map - The structure used to represent a folksonomy.
As relatively new ideas, these definitions are not used consistently across the literature.  My definitions are designed to make analysing the concepts easier, but for a better understanding, Thomas Vander Wal's definition is probably the most authoritative and wikipedia 's definition probably represents common usage of the terms.