I have heard there is a difference between movies 'based on' verses those 'inspired by' true events. Does one relationship with the 'true events' have more license than another, or is it just the director's discretion as to which phrase to use?
Both are sufficiently vague that the author can use them however he/she wants. Both wordings could mean anything from "nothing like the actual events" on up to "exactly like the actual events".
So the director / author can and will decide which best fits their marketing motivations, in a matter of connotation and style.
I could imagine that a more artistic movie would use the term "inspired by", and an action movie would connect better with "based on" for example.
Outside the context of art, I think "based on" does imply a closer resemblance to fact.
In common use, based upon a true story means that the essential trajectory of the actual story remains intact. The author/screenwriter may have made significant adaptations -- renaming characters, shifting the location in time or space, exchanging genders, compositing several real people into a single representative character, and so forth -- but the core of the story remains the same.
Inspired by a true story, on the other hand, generally means that an actual event was used only as a sort of springboard for the finished work; a "what if" scenario, if you will. Often some very significant changes are made -- the murderer hanged in real life may get away with the crime, or vice versa. It is often an indication that the writer is using a situation familiar to the audience as a stepping stone to exploring an issue they might not otherwise have considered.