A Tag is a label attached to information (and more). A tag is the name of the artist who made a grafitti painting . We do use labels and tags to improve finding bits of information.
Tags are used to get an overview in a text.
Hashtags (a tag with a preceding hash sign #) are used on Twitter, and they have the same function as tags. They are intended to threading. Hashtags are also used in coding.
This twitter message has two hashtags, #ds106 and #umwds10614. These hashtags are intended to add the message to two streams of messages. The #ds106 hashtag is intended to add this twitter message to all other messages in the #ds106 stream. People could search (in twitter) this hashtag and find all messages with this hashtag.