Fuel is a substance which on burning releases a large amount of energy as heat at a reasonable cost and leaves behind little ash content. For example, coal, natural gas, petroleum nearly meet all these conditions.
A combustible substance is one that can burn. It does not necessarily mean that it would produce a large amount of heat without leaving any residue. Thus all fuels are combustible but not all combustible substances are fuels.
All the combustible substances are not fuels because many of them produce less amount of heat for a particular amount of energy input on burning and leave behind high ash content; for example, paper, cloth, etc.
A good fuel produces large amounts of energy and does not leave behind any undesirable substances. Also, it is cheap and is readily available.