Fire is what we observe when a chemical reaction called a combustion reaction occurs. I’m not sure if I would classify fire itself as a state of matter. The heat and light we observe from a fire is a form of energy transformation. Namely, the potential energy stored in chemical bonds being transferred to heat and light. Generally, in a combustion reaction some kind of fuel and oxygen react to form byproducts gasses (usually something like CO, CO2, but it depends on what the fuel was), and the “leftover” energy which isn’t used to break and reform chemical bonds is released as heat and light. I would consider “catching fire” and “combusting” to be synonyms in a chemical sense, at least.
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