I’ve never heard of folksonomy and it is interesting to know such term, which is first coined by Thomas Vander Wal. According to wikipedia, folksonomy is also known as
collaborative tagging, social classification, social indexing, and social tagging.
Image credit to Flickr user: Ross Mayfield
As you can see from the image, the tags, which build the folksonomy in social media is always public, which means that everyone or members of a community can view them. However, only I can view the tags that I use in my mail or other private sites.
Image credit to Flickr user: Andrea Hernandez
In contrast with taxonomy, folksonomy does not have any hierarchy and usually uncontrolled. In other words, the tags in folksonomy might have different meanings related to it. Or other different words or tags have the same meaning.