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.