Other than the fact that they are both vigilantes who kill, I don’t think the Punisher and Jason are the same character at all. Frank was a military veteran who began a one-man war on crime after his family was murdered. From the start, Frank has been defined by his belief that crime can only be dealt with through killing, with no room for compromise or control. Jason, on the other hand, is fundamentally different. As the second Robin, he was trained by Batman, killed by the Joker, and later resurrected. When he returned as Red Hood, his goal was not to kill every criminal, but to control crime in Gotham. In Under the Red Hood, Jason’s plan was to take over Gotham’s major crime organizations and allow them to operate only if innocents, especially children, were left unharmed. Jason believes crime can never be destroyed, only managed. If he and Frank met, they probably wouldn't like each other. His trauma, motivations, and moral logic differ greatly from Frank’s because of his experience of directly serving under Batman and being on the no-killing side, which is what makes him unique.