I'm not sure which 'Logan' you specifically refer to. There could be many people named Logan. It could be a common name for an individual in a story, a character in a movie like 'Logan' where he is a mutant with a complex and tragic backstory involving his powers, his family, and his struggle in a world that often fears and hunts mutants. But without more context, it's hard to tell the full story.
Old Man Logan is set in a dystopian future. In this world, the villains have taken over. Logan has given up his violent ways and is just trying to live a quiet life on his farm. But when he's forced to go on a journey, he has to face his past and the new threats. He teams up with Hawkeye, and together they battle through a landscape filled with old foes who are now in control. It's a story of redemption and facing one's demons.
If Logan is the Wolverine, his powers are a key element. His adamantium claws and rapid healing ability shape many of his adventures. Also, his relationships, like his complex friendship with Professor X, are important parts of his story.
The main events start with Logan living a quiet life on his farm until something forces him to leave. Then, his team - up with Hawkeye is crucial. They face off against the villains who have divided up the country. Also, Logan's struggle with his own past and his decreasing healing factor are important events throughout the story.
Well, Deborah Logan isn't a completely true story. It's likely a blend of fictional elements and perhaps some loose ties to real-life situations or themes.
Logan Lucky is purely fictional. The story was crafted for the big screen and doesn't have any roots in actual happenings. It's all about delivering an enjoyable cinematic experience.
Logan is loosely based on the comic book character Wolverine from Marvel Comics. It takes inspiration from various storylines featuring the character but presents a unique and darker take.