This is a fantastic question!!! A lot of materials are actually both. This is because the way a conductor works is by the little bits that make it up (molecules) bumping into one another and passing along the heat, a bit like a Mexican wave. This is why solid things like metals, where all the molecules are close together are good conductors and things like polystyrene with lots of air in it which means the molecules are far apart are good insulators. What this means is that you might have something which is a good conductor when it is a solid or liquid (such as water) when the molecules are close together, but an insulator when it is a gas and the molecules are far apart.
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