The introduction of a story can also be known as the 'start-up'. It's that part that hooks the reader and gives them an initial idea of what the story is about.
Another name for it is the 'prologue'. Usually, it sets the stage and gives some background for the main story to unfold. Also, it might be referred to as the 'preface' in some cases.
A yarn can also be another name for a story. This term is often used in a more informal or folksy way. People might say 'spin a yarn' which means to tell a story, usually one that is interesting or perhaps a little exaggerated.
A chronicle. A chronicle is more like a record of events in the order in which they occurred. However, it can also be seen as a type of story, especially when it is told in a more engaging and narrative way, like historical chronicles that describe the lives of people and the events of a particular time period.
A short story can also be called a novelette or a short narrative.
Another name for plot in a story could be'storyline'.