Inspired By

"Anything can be 'inspired' by a true story! One day I pooped to the moon. INSPIRED BY A TRUE STORY??"

Hollywood dialect for "Research is hard." Semi-intentional Adaptation Decay applied to a true story.

Indicated in Law & Order commercials by the phrase "Ripped from today's headlines!"

Examples of Inspired By include:

Film

District 9 was inspired by the real life forced removal of over 60,000 blacks from District 6 in Cape Town.
Troy was "inspired by" The Iliad according to its credits. Pretty accurate assessment.
The movie Eight Below features an American team of eight sled dogs, six of whom survive for six months in 1993. It was "inspired by" a Japanese team of fifteen dogs, two of whom survived for one year in 1958.
Headless Body in Topless Bar took this to its logical conclusion: the title was Based on a True Story (a headline in The New York Post), and the rest of the plot was extrapolated from it.
Leatherface in The Texas Chainsaw Massacre, Norman Bates in Psycho, and Buffalo Bill in The Silence of the Lambs were all loosely inspired by real life serial killer Ed Gein. Comparing and contrasting those three characters should give you an idea of exactly how loosely. (For the record, Buffalo Bill is probably closest to the real guy. Frighteningly, Leatherface is arguably closer than Bates.)
Unstoppable was inspired by the "Crazy Eights" train incident in Ohio in 2001.

The basic premise of M. Butterfly was Ripped from the Headlines, but the playwright intentionally did little research on it, because he wanted a completely fictional play. By way of honesty, he also changed the names to protect the innocent.

Katawa Shoujo was inspired by a single sketch. Originally it wasn't even coloured.