Tesla coil produces AC or DC spark output?
The output from a tesla coil is indeed ac but it's a lot higher than 60Hz. Using a 50 or 60Hz supply is convenient because it has the power to generate a decent charge into a capacitor that connects through to the primary via a spark gap. See this explanation for starters.

The primary coil (via the spark gap) resonates with the primary capacitance and this forms a parallel tuned circuit. For high-Q parallel tuned circuits, the current that flows between primary coil and capacitor is very high and usually tens to hundreds of kHz.

This generates an alternating magnetic field that impinges on the 2nd coil. This second coil has much higher Q than the first coil and is tuned by the capacitance of the large terminal to ground. It is also a parallel tuned circuit and when tuned to be at the same frequency as the primary resonance produces rather large voltages that most of us have seen on videos.

All this happens at very much larger frequencies that AC mains. Normally, on tesla coil demonstrations, a medium voltage dc supply is used to charge C1 up to the voltage needed to break-down the spark gap.

As an aside, I've used low voltage tesla coils (tuned primary and secondary coils) to couple useful amounts of energy across a 40mm gap to power electronics on a rotating machine. OK they don't use the spark gap to initiate a spark but they do use exactly the same principle. There is also a lot of talk about using this technique to power lamps wirelessly. I don't think it will replace wires though because energy transfer is fairly inefficient.