I've been in the "movie industry" for decades and it still astounds me that people come out of the theater thinking what they saw, in most cases, is reality--even when the disclaimer "based on" is clearly shown ahead of time.
I can't exactly fault them as "based on" seems to be more of a marketing gimmick used to imply some form of authenticity rather than an actual disclaimer. For the longest time I fell for the fallacy that "based on" implied some semblance of factual accuracy.
Something that is inspired by something is also based on that thing.
This seems false? If iPhone was inspired by Blackberry (no idea if it was) that doesn't imply iPhone was based on Blackberry.
Inspire -- give rise to -- stimulate, motivate, spawn, engender.
Based on -- rooted in -- built upon, be founded on/upon, be anchored in something, rooted in.
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A hamburger inspired the design of the Millenium Falcon, the ship is not based on hamburgers. A comic book inspired the movie 300, which is only loosely based on the comic and historical fact.
A story that is based on specific events it must build upon those events. A story that is inspired by something has no presumption of content, only that some facet of it motivated the storyteller somehow.
So while, yes there is nuance, they still broadly mean the same thing: you actually just gave two examples agreeing with me.
And directly conflicting definitions are not "nuance". You are missing a qualifier in order to make the point you think you're making (ie "the design of X is rooted in..."). You've also wilfully read past both examples in order to stretch this point.
Inspiration can not be understood as "rooted in". That is not how words or sentences work. The millenium falcon is not rooted in Hamburgers. "Imagine" is not rooted in Yoko Ono.