DC is a constant, AC 60Hz 16.67mS per cycle or every 8.335mS is a zero crossing, 50Hz 20mS per cycle or every 10mS is a zero crossing.
Current has a profound affect on gap spark, as this is used in proportion to voltage applied and relays, circuit breakers are made with specific ratings. If the current is minimal and voltage large the gap would still need to be larger for DC, same if the current is over voltage. Compared to a AC relay of about the same rating the gap would be somewhat smaller. Although I have relays that can use both AC and DC on the switching side usually the DC rating is alot smaller than the AC equivalent, this does not apply to Solid state relays as the must be made for AC or DC.
Jacob's Ladder, we are talking high voltages here like in the kilo volt range 2kVac. If you applied 2kV DC on a dead short across the Jacob's Ladder using a piece of wire (most likely the wire would vaporize to break short) to the gap required for AC ionization the DC spark would jump at the narrowest part of the ladder and continue to do so untill the gap is broken or to wide to allow DC to pass.
Alot of things change and the physics of electricity bend as we get into extremely high voltages.