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When heating up a material, the energy can go into two places, increasing the temperature (specific heat), or changing the phase (heat of vaporization). Steam may not be more hot compared to boiling water if they are both 100ºC, but it will be carrying more energy because of the energy input in order to change the phase. This energy can be released without changing the temperature of the steam, but it will turn into water.
Essentially steam carries more energy as it takes a lot of energy to transition from liquid to vapor. So while they may have the same temperature, steam will very likely have a higher heat content due to the heat of vaporization as you mention.
For a more visual representation through the heating curve of water, you can see that transitioning from liquid to vapor requires a lot more energy than it does from solid to liquid. Thus, steam carries more heat than boiled water.
The energy needed to from boiling water to steam is quite high. While steam and boiling water may not have a considerable difference in temperature when the steam cools down it will release a lot of energy as it condenses, because when the steam was formed it needed a lot of energy. When that steam condenses onto your skin it burns more severely, because its releasing a lot of energy.
In order to break the hydrogen bonds found in liquid water, quite a bit of additional energy is required to be added to change water's phase from liquid to gas. This energy stays with the vaporized water molecules and it is released when it condenses back to liquid.
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