Warning! Spoilers for The Boys comic book and television series below
Homelander's dark nickname and origin made him The Boys twisted version of Wolverine, as the Supe had a very similar purpose for receiving his powers as the X-Men hero when he was experimented on during the Weapon X program. In The Boys comic book series, The Legend refers to Homelander as the Living Weapon, showing that he was made to kill and do the bidding of his creators, much like Logan was.
In the comics, Wolverine was born a mutant with incredible powers, including retractable bone claws, an impressive healing factor, super strength, and other enhanced senses. However, after being captured by the Weapon X program, Wolverine was experimented on to become a living weapon to carry out the missions of the government organization. As a result, Wolverine's bones were coated in adamantium, forever changing the hero. Much like Logan's origin, Homelander from The Boys was designed to be a living weapon, as he's given the nickname by the man responsible for crafting his PR stories.
In The Boys #20 by Garth Ennis, Darick Robertson, Simon Bowland, and Tony Avina, the universe's version of Stan Lee, The Legend, reveals the secrets of Homelander to Hughie, going through the Supes' made-up origin and the real nature of his existence. In their conversation, The Legend refers to Homelander with the nickname, Living Weapon, adding that he was created to be Vought-American's weapon, including taking out other heroes who stepped out of line. Much like Wolverine, Homelander was experimented on to become a weapon of their respective creators, Weapon X and Vought.
Homelander and Wolverine took two different paths after becoming a "Livin' Weapon," as The Legend nicknames the Supe. Logan would overcome his Weapon X programming and become a force of good, ing the X-Men and becoming one of its most important heroes. Homelander, meanwhile, embraced being a weapon for Vought-American and became one of the deadliest beings in The Boys universe, killing his fellow Supes and anyone who else dared to defy his or Vought's orders. He was exactly what Weapon X wanted.
Funny enough, Homelander actor Antony Starr, who plays the psychotic Supe on The Boys, has been among the top of many fan casts for the new Wolverine in the MCU. Still, regardless of whether the actor will eventually play both characters, the dark nickname given to Homelander forever connected him to Wolverine, as the Marvel hero's time with Weapon X as a living weapon isn't dissimilar from The Boys hero's time with Vought-American. But, ultimately, the living weapons ended up going in different directions from how they were created to be.
