This is an interesting question, as these are certainly different words that can be used in different ways, and yet most dictionaries blur any distinction.
I agree with Ronan's answer, but a key difference might be causation:
If an author writes, "The king died and then the queen died," there is
no plot for a story. But by writing, "The king died and then the queen
died of grief," the writer has provided a plot line for a story.
A plot is a casual sequence of events, the "why" for the things that
happen in the story.
As such, "The king died, then the queen died, then..." could be thought of as a storyline, indicating a series of events much as a history timeline does, whereas "The king ate an apple that had been poisoned by his brother. The queen, upon finding his body, went into a state of despair and gradually died of grief" is a plot.
The Wikipedia entry has the following relevant entries to which "storyline" may refer:
- The plot or subplot of a story;
- The narrative of a work, whether of fictional or nonfictional basis;
- The narrative threads experienced by each character or set of characters in a work of fiction
"A narrative (or story) is any account of connected events, presented
to a reader or listener in a sequence of written or spoken words, [...]."
"A narrative thread, or plot thread (or more ambiguously, a
storyline), refers to particular elements and techniques of writing to
center the story in the action or experience of characters rather than
to relate a matter in a dry 'All knowing' sort of narration. Thus the
narrative threads experienced by different but specific characters or
sets of characters are those seen in the eyes of those characters that
together form a plot element or subplot in the work of fiction. In
this sense, each Narrative thread is the narrative portion of a work
that pertains to the world view of the participating characters
'cognizant' of their piece of the whole [...]."
We all know the issues inherent in blind faith in Wikipedia, but the distinction made there is an important one: what one might think of as a "storyline" is described on Wikipedia as a "story", while "storyline" is either synonymous with plot or is a character/narrator-prescribed element of plot.
I also looked for clues on etymonline but found only that "timeline" is from 1876, from, of course, time + line, and "story-line" was first attested 1941. It is possible that the latter was constructed as the narrative equivalent of a timeline; it is of course also possible that it was used as a synonym of "plot" right from the start.
It would seem that any distinction currently comes down to subjective opinion/interpretation. In my own studies in the field of narrative theory, I have not seen any particular concern about the need for a distinction. It might pay to consult writing guides or head over to https://writers.stackexchange.com/ to get field-based thoughts on this. A Google book search will also give you some real-world usage examples.