People have been doing Prisoner's Dilemma with different payoff amounts since the dawn of PD, and of course this can result in qualitatively different strategie

People have been doing Prisoner's Dilemma with different payoff amounts since the dawn of PD, and of course this can result in qualitatively different strategies. But sticking to just the rules, rather than the results. Is is the snowdrift game just a payoff score tweak? Or is there some structural difference that I missed?