Burning takes place at a very high temperature whereas rusting takes place at low temperature.
Rusting and burning are oxidation reaction processes in the presence of oxygen. But water is essential for rusting as it could prevent burning.
A high profile difference between rusting and burning is that rusting is a very slow process that could take many days while burning is a rapid process that could consume materials in minutes.
Rusting is associated with iron and materials containing iron, burning is associated with diverse materials that may include materials containing iron.
Both burning and rusting are exothermic processes as heat is released during both processes. But the heat released by rusting is undetectable as it is released slowly in small amounts over a long period of time. Whereas, heat released from burning is in large quantity and is released in bulk within a short period of time so that it is detectable