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Something that is projected, usually at great speed, from the muzzle of a gun or similar.

Could be a shell or bullet.

Differs from a missile for some technical reason which escapes me.

BMGs guess: A missile carries its own form of propulsion whereas a projectile gets all of its propulsion from the big bang in the gun - i.e. a missile goes whoosh - a projectile goes bang.

A projectile is any form of object powered through a void by the application of an external force. We tend to use the term for any unpowered object i.e. lacking an on-board motor, such as an Artillery shell or a mortar bomb. A fin round is also a projectile. Any unpowered externally forced projectile follows a ballistic trajectory - however small it may seem, as BMG alludes to above. We can see, therefore, that technically speaking, a misssile could be classed as a projectile if it relies on motors cutting at some point during its flight and then following a ballistic trajectory to earth. An example of this is the V-1 which literally dove to earth on the point of a ballistic trajectory - it was not steered (or 'guided') in any way. V-2 was not - it was powered all the way to its objective at (local) Mach 3. {I think you have this the wrong way round. The V1 was a cruise missile. It flew in a non ballistic trajectory because it was a small aeroplane until the fuse system activated, cutting the engine and setting the control surfaces so the V1 would dive to earth. The V2 flew in a ballistic trajectory after about 70 seconds of rocket engine thrust. pteranadon)
Rockets are also (technically) projectiles, however the term 'rocket' is usually reserved for free flight i.e. unguided rockets, like FROG 7 (Free Rocket Over Ground), whilst 'missile' is reserved for guided systems. Like all good rules, there are literally tens - if not hundreds - of examples that disprove this, such as the Multiple Launch Rocket System (MLRS) which has a 15m CEP or Guided MLRS (GMLRS) with a unitary warhead - it has a CEP of 7m derived from GPS.