They’re all based on the same real man.
They are all only partially based on aspects of his life. To get the true effect of Gein’s madness, you have to look at the movies together. Like Bates, Gein was obsessed with his mother; like Leatherface, he butchered human beings for parts; and like Buffalo Bill, he was confused about his gender identity and wanted to become someone else.
In 1958 his crimes came to light when authorities stormed the Gein homestead. What they found revolted and horrified them.