If the 'Wild Bill' in 'Wild Bill the True Story' is not Hickok, it could be some other local hero or character. There were many people in history with colorful nicknames. This 'Wild Bill' could be someone who had a significant impact on the community where the story is set, perhaps a man who fought against injustice, or who had some remarkable feats that made him stand out in the local lore.
In most cases, 'Bill the Bastard' isn't a true story. It could be inspired by real events but with significant alterations and imaginative additions to make it more engaging.
I'm not sure specifically who 'Bill Williamson' in a 'true story' is without more context. There could be many people named Bill Williamson. He could be an ordinary person whose story was told in a local context, like a small - town hero or someone with an interesting personal journey.