After his cosmic snap killed half of all life in the original Infinity Gauntlet comic event, Wolverine and Hulk were secretly recruited to kill Thanos, coming closer than any other hero to ending the threat of the Mad Titan. Created by Jim Starlin, George Perez, and Ron Lim, Infinity Gauntlet saw Thanos gain the power of the all-powerful artifact and promptly kill off half of all life as a tribute to his beloved Death, before challenging the fundamental forces of the universe in a bid for godhood.
Unlike in the MCU's Infinity Saga - where Thanos is played by Josh Brolin, and Wolverine does not exist in continuity - the Avengers only truly banded together to face Thanos once he already had all the Infinity Gems and had performed his famous snap. Warned of Thanos' plans by the Silver Surfer and gathered together under the leadership of Adam Warlock (likewise absent in the MCU), Marvel's heroes began making plans to confront Thanos and take back the Infinity Gauntlet, restoring their fallen allies and fixing the damage done to the cosmos. But while Captain America was rounding up international allies for the battle ahead, Wolverine and Hulk were taken aside for a darker proposition.
Hulk initially resisted the Avengers' call for help, feeling out of place with more traditional heroes during a particularly dark period in his adventures. But brooding on the roof of Avengers' headquarters, Hulk is approached by Wolverine, and the two bond over being "monsters" surrounded by heroes. It's then that they're approached by Adam Warlock, who explains that while Earth's heroes will attempt to stop Thanos without loss of life, he believes that the Mad Titan is too powerful to treat like a traditional supervillain, and that "extreme measures may be called for in dealing with him." He asks that if the opportunity arises, Hulk and Wolverine kill Thanos, with Hulk replying, "You're a bit of a monster yourself, aren't you, Goldilocks?"
When the heroes face Thanos, Wolverine and Hulk both do their best to take him down. Hulk attacks without reservation, but it's Wolverine who truly goes in for the killing blow, sneaking up behind Thanos as he's battling Thor and Firelord (a former herald of Galactus), and stabbing him through the chest with adamantium claws. Sadly, the Infinity Gauntlet has made Thanos too powerful, and he shrugs off what should have been a deathblow before mangling Wolverine's body and moving on to the other heroes.
Thanos would eventually be defeated by a combination of Mephisto's scheming, Nebula's theft of the Infinity Gauntlet, and Adam Warlock's decision to take its power for himself, but Wolverine and Hulk's secret plan to kill Thanos shows a huge difference between The Infinity Gauntlet and the big-screen pseudo-adaptations Avengers: Infinity War and Avengers: Endgame. In the MCU, Thanos is decapitated by Thor after wiping out half of all life - a move that shocks the rest of the Avengers but is quickly accepted by the team - and his earlier self is later faced in an all-out, life or death battle in which the heroes triumph.
In the comics, the heroes are a little more traditional in their outlook, seeing killing as monstrous, even when it's a villain as vile as Thanos. That Wolverine and Hulk are approached for this secret role, and that Logan definitively tries to go through with it (albeit after seeing the extent of Thanos' power), sets them apart as heroes genuinely darker than the Avengers, as well as depicting Adam Warlock as a less straight-forward hero than someone like Captain America. While Wolverine and Hulk weren't able to kill Thanos (who faked his death at the end of Infinity Gauntlet, and vowed to live a life of peaceful contemplation), the fact that they were approached to do so shows that they'll always be a little apart from Marvel's other heroes - willing "monsters" prepared to cross lines that other won't, even if it leaves them soaked in blood.