Suefic

A Suefic is a story, often a fanfic, in which the main character is a Mary Sue. More than that: the story revolves around the Sue. Often, there is no plot beyond the Sue finding out about all her uncanonical powers and falling in love with the character that the Suethor thinks is the most attractive.

Alternatively, a Stufic is about a Marty Stu who finds out all his uncanonical powers and saves the day in the most awesome way the Stuthor can think of.

Most, if not all, Sue- and Stufics are written by young or inexperienced writers. They are essentially daydreams written down.