Combustible is a technical term and is used much more frequently than "burnable".
In fact, I have seldom seen the word burnable.
Technically speaking, combustible is often defined as something that will burn at or above 38 degrees C (100 degrees F).
However, materials that will burn at temperatures below 38 degrees C (100 F) are usually referred to as "Flammable". Some flammable materials (usually liquids and gasses) burn even at temperatures as low as [-43 degrees C gasoline] and [-60 C butane].
Years ago, English speakers used the word "inflammable" to mean "flammable". Strange, because one would think that "inflammable" might mean "not flammable" due to the prefix "in". The word "inflammable" is not used very often any more.