Fire requires four things to live. Heat, fuel, oxidation, and a chemical reaction. Since mater cannot burn in a solid state, it must be converted to a gas.

Converting a solid to a gas is known as pyrolisis. This requires heat. Different amounts of heat are required for diffrent types of matter. For example, a solid 2×4 will require more heat to convert than would sawdust.

The fuel itself is matter. Newton’s law of the Conservation of Mass & Energy states that matter is not created nor destroyed, it only changes state. So for fuel to burn it must be converted to a vapor.

Oxidation or oxygen is required in order for a fire to breathe. Some products require less oxygen to burn and others more. Our atmosphere is 21% oxygen and readily supports the combustion process. But, there are other products such as peroxides, and nitrates that release their own oxygen as they burn thereby supporting the combustion process with less oxygen.

The chemical reaction happens when the other three, heat, fuel and oxygen are brought together in the correct amounts and either through an outside ignition source or self ignition, the four produce a flame.

As various elements in a product are converted to a gas and burn, they give off varying degrees of light and color. Carbon is present in every fire and thus produces carbon monixide, one of two volitile gases that cause smoke inhalation. The darker and heaver the smoke, the more incomplete the combustion. Likewise the more complete the combustion process, the closer to white the flame is.

So all this boils down to this…. Rust is oxidation. As a pice of metal rusts, it is producing heat, giving off it’s own oxygen, converting the fuel, and a chemical reation with the air and metal is happening. This is all on the very slow end of the spectrum. On the fast end, you have fire. Fire speeds up the process all based on the type of fuel, amount of oxygen, amount of heat and the speed of the chemical reaction.

Hope this helps.
References :
Firefighter/Instructor 21 years