These stories are time loops where the character relives a time period several times, starting over each time. The most famous of these are Groundhog Day starring Bill Murray, a movie so known for this type of time travel that most movies or television shows with a person stuck in a time loop references the movie or is described as being like that movie.
Based on the Novikov self-consistency principle, the stories have “fixed” timelines with no possibility of paradoxes. Present actions affect the future AND the past, which must also affect the present. Everything being done is caused by everything being done. It is as if the time traveler is a “gear” or "cog" of a bigger “machine.” Some ways to make this plot work is to make the future events questionable as to whether they would have happened with or without the time travel.
These stories allow for tangent timelines, but certain events hold so much “gravity,” that they will happen even if something changes. Trying to change a big event is nearly impossible. Many of these stories seem to be the "Cog" type at first.
Stories about a group of people trying to keep people from changing the past.
Lost in TimeEdit
Stories the overall plot is about a person or people ending up in a place in the distant past or future.
Out of OrderEdit
Stories about living life out of order.
Stories that feature time traveling superpowers.
Based on the many-worlds theory that changes, even small ones, create a new timeline and set of events. Most time travel stories fall in this category.
Stories about traveling time as someone would travel the world or space.