Is Jaws a true story?
No, at least not in the words of Peter Benchley, the author of Jaws, even though he was undoubtedly aware of the 1916 assaults (they are mentioned in his novel). Although Jaws is not based on a true occurrence, reputable news sources frequently point to the 1916 shark attacks in New Jersey as the film's primary source of inspiration.
Are there any cool movies about sharks that are real stories? Not documentaries.
I can recommend several shark-related movies based on real stories:
Open Water (2003):
Based on the story of Tom and Eileen Lonergan, who traveled with a scuba-diving group to the Great Barrier Reef in 1998 and wound up stranded when the group’s ship left them behind after taking an inaccurate headcount. 
The Reef (2010):
Based on the story of Ray Boundy, who survived an incident where his boat was capsized and a tiger shark killed two of his crew mates.
Soul Surfer (2011):
Based on the story of Bethany Hamilton, a young girl from Hawaii who lost her arm after being bitten by a 14-foot tiger shark while surfing and then courageously made her return to the sport.
Kon Tiki (2013):
Based on the adventure of Norwegian explorer Thor Heyerdahl, who in 1947 wanted to prove that it was possible for people from South America to sail to Polynesia 1,500 years ago.