Sure, Billy Bathgate is fiction. It falls within the realm of creative writing, where the author weaves a tale that may or may not have any resemblance to reality.
Once upon a time, there was a little rabbit named Benny. Benny lived in a beautiful meadow filled with colorful flowers. One day, Benny decided to go on an adventure. He hopped over a small stream and found a big, old oak tree. Under the tree was a hidden door. Benny was curious and opened the door. Inside, he found a whole new world full of friendly forest animals. They welcomed Benny and he had a great time playing with them.
Yes, Billy the Kid was a real person. He was a notorious outlaw in the American Old West. His real name was Henry McCarty, and he was involved in various criminal activities, including cattle rustling and murder. His life and deeds have been the subject of many stories and legends.
Billy Elliot is based on a true story to a certain extent. It incorporates real elements but may have fictionalized parts to enhance the drama and entertainment value.