In simple terms power has two components, voltage and current. With direct current (DC), the power is the voltage times the current. For a given amount of power, you can have low voltage with high current, or high voltage with low current.
Tesla coils take a modest amount of power and raise the voltage, but at the cost of lowering the current. In the end, the power is the same, but expressed differently.
Soldering irons go the other way, they take a certain amount of power and lower the voltage, but raise the current.
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