Are voltage and current the same when it comes to device protection?
Damage is created in semiconductors when the dielectric breakdown triggers a negative resistance current breakdown.  But ESD diodes are typically small and faster so only rated for 5mA so they use 2 stages of D:R impedance ratio using 10k to limit transient current and diodes limit incoming voltage thus SCR current latch up effect. SCR effects trigger with negative resistance fold back and rising current with reducing voltage, thus negative slope.
TVS protection shunts with very low Rs better but depends on source impedance of V=Q/C and ESR of source ( ESD vs lightning)
So damage is protected by impedance ratios to reduce current going in with series R to bypass diodes to Vdd,Vss or TVS to ground.  Thus higher current yields higher voltage from incremental conduction of diode law but is logarithmic then cascade effects attenuate further.
also C ratio of source matters as C has some finite ESR which affects voltage transfer ratio.
So Voltage is the trigger, but follow-on current does the damage.
Power line grids use ground wire above Line then air gap arc SCR like suppressors to shunt over voltage on Line. Dual protection.

ground wire and tall wire antenna act as deflectors of E field to shunt bypass arc to ground.

then Arc suppressor air gaps shunt line voltage transients to prevent arcs down the grid to local bypass to gnd.