The difference - in theory - is social democracy preserves private property (and therefore capitalism) while democratic socialism does not. Has Mamdani abolished private property in New York City, or does he plan to before his term as mayor ends? If not, then there is no practical difference between a social democrat and a democratic socialist in our current context except perhaps in the vision that is offered. The fact is that reorganizing a capitalist society to be socialist is not possible by electoral means alone; doing so requires that workers organize to seize the means of production for themselves independently of the state. An elected official that is truly committed to a democratic socialist vision may support workers in their efforts to do so, but there’s nothing they can do on their own to make it happen. Mamdani might truly believe in a democratic socialist vision, but what he is practicing as mayor is social democracy and nothing more because that is what is feasible for an elected official to accomplish. Even a vanguardist revolution cannot accomplish more without the people organizing on their own (and historically I would argue that they haven’t sufficiently done so, resulting in AES being social democracies at best, and autocratic state capitalist regimes at worst).