Electrostatics, planar-magnetics, ribbons, horns.
But it’s not just the snare wires you’re hearing, but also the wires vibrating against the resonant (bottom) head on the snare drum.
As an aside, to hear what a snare drum sounds like with the snare wires disengaged (via the drum's "throw-off"), give a listen to "Tears Of Rage" by The Band.