In the story, a fact is that Buddy Holly had a unique sound that was a blend of different musical styles. However, the movie might have fictionalized some of the events leading up to his big breaks. It might have made it seem more linear and easy-going when in reality, the music industry was very competitive and full of setbacks for him. He had to really fight for his place in the music world.
The fact is that Buddy Holly was a pioneer in the rock and roll genre with his innovative use of instruments like the Fender Stratocaster. Regarding fiction in 'The Buddy Holly Story', perhaps the movie exaggerated the extent of his immediate popularity across all demographics. In reality, his music grew in popularity gradually among different groups, but the movie might have made it seem like he was an overnight sensation everywhere. His journey to stardom was a long and winding road with many small steps and a lot of hard work.
Well, in the Buddy Holly Story, one fact is his real musical talent and his influence on rock and roll. Fiction might be some overly dramatized parts of his relationships in the movie. For example, his actual relationships with his bandmates were more complex than what was sometimes shown on screen.