In the comics, "The Spider" (Spider-Man Noir) is Peter Parker, whose Uncle Ben—a World War I veteran—is murdered by criminals working for industrialist and crime lord, Norman Osborn, a.k.a. the Goblin.
With the words his uncle told him ("If those in power can't be trusted, it's the responsibility of the people to remove them") guiding his actions, Peter ventures into a warehouse of stolen antiques and finds a spider idol. When it breaks, it releases a horde of spiders, one of which bites him and grants Peter powers. It's heavily implied that his abilities are mystical in nature, as he dreams of a spider-god while unconscious.
In Prime Video's Spider-Noir, things play out a lot differently. In flashbacks, it's revealed that Ben Reilly helped free men who were being experimented on during the Great War. They're restrained in beds that are linked to various creatures, including a praying mantis, a snake, and a lizard.
One prisoner has been transformed into a monstrous Man-Spider, who is, as you might expect, part-human, part-spider. He bites Ben's arm before he's shot, and after everyone is freed, a frantic Ben orders that the whole place be burned down.
We learn that a scientist, Dr. Faber, was behind the experiments for a failed super-soldier program that the Germans were running. Initially, Ben gave in to his new spider-like nature, but managed to repress that and become more human. Able to push down his tics and impulses, he gains organic webbing and all the expected Spider-Man powers. To relearn how to be human, he went to the movies and studied classic film actors.
The prisoners in Faber's care were injected with irradiated materials and are now dying, getting closer to death each time they use their powers. While the Germans wanted to create superpowered soldiers, Faber wants to save her son and creates an antidote for the show's villains that factors heavily into Spider-Noir's finale.
The reason Ben isn't dying is that he was bitten, not injected, but this wild new origin story is certainly unique. It also gives Nicolas Cage the chance to go to some really bizarre places with his performance.
It's also revealed that Ben's late wife, Ruby J. Williams, was the one who taught him, "With great power comes great responsibility." Of course, the private eye is more interested in having no power or responsibility when this series begins.
Spider-Noir is now streaming in its entirety on Prime Video.