What is the difference between a 'rocket' and a 'missile'

Someone pointed out on the BBC News that the Malaysian plane was hit not by a 'rocket' but by a 'missile'. From the dictionary definitions I have looked up I cannot tell the difference.

Missile An object which is forcibly propelled at a target, either by hand or from a mechanical weapon.

Rocket a cylindrical projectile that can be propelled to a great height or distance by the combustion of its contents...

Oxford Dictionary of English

Is it therefore the case that a rocket is always a missile, but that a missile is not necessarily a rocket? A cricket ball can be regarded as a missile but is clearly not a rocket. But why could the type of weapon which it is believed brought down Flight MH17 not be described as a 'rocket'?

A rocket is so called on the basis of its mode of self-propulsion. A missile is so called on the basis of its being propelled, by a rocket engine or otherwise, for the purpose of doing damage, as a weapon. The two categories overlap considerably, since rockets are commonly used as propulsion for missiles, with or without in-flight guidance systems. Put an explosive warhead on top of an Atlas rocket, and launch it at an enemy (or practice target), the whole assembly becomes a missile. Put a Mercury capsule on top with John Glenn inside, it is a rocket but not a missile. The weapon that reportedly brought down the Malaysian airliner was (or is, if considered generically) both a rocket and a missile, and can properly be termed either one—though without the explosive payload that transforms it from mere rocket to missile it would probably not have brought the plane down, so missile is the more adequate term in this case.

There's a further definition for missile:

a weapon that is self-propelled or directed by remote control, carrying conventional or nuclear explosive

Emphasis mine.

While rockets have been and still are used as weapons, the word rocket does not convey the sense of being guided that missile does.

Summary: a rocket is a means of propulsion; a missile is something that is propelled (possibly by a rocket).

A rocket is an engine that propels an object by combustion, where both the both the propellant and oxidizer are contained in the engine, as opposed to being input from outside (e.g., the oxygen does not come from the surrounding air or water).

A missile is any object that is propelled (typically in 3 dimensions, as through space, air, or water).

Some missiles are propelled by an exterior force, and after that initial push are simply ballistic: falling. Others have an on-board engine: they are self-propelled. A combination would be essentially just falling but with one or more small engines on board that can change the trajectory slightly.

Of the latter (missiles with on-board engines), some have self-contained engines; others can make use of oxygen in the fluid they pass through. Of those that have engines, the best known have rocket engines.