Terms are the basic unit or smallest item in Managed Metadata or Taxonomy. TermSet is just a collection of Terms.Like say if you want to create a taxonomy for countries and their cities.
Country will become the TermSet (eg:England) and cities will be Terms inside respective termsets ie London will be term inside England.
Tags are special terms , they are stored inside Keywords termset in a internal taxonomy group System. You can add tags to documents and pages.After tagging with the help of tag cloud you can easily track documents, pages and other activities.
#HashTags are again special terms stored in HashTags Termset in System taxonomy group.#Hasttags can be used in newsfeed , blog posts, discussions etc, to make them more social.It is very much similar to twitter,FB social hash tags.
OOTB tags & Notes always works with Keywords termset and hence you can only create tag and add tags from Keywords termset only.
See this article for Tags & Notes