Missile usually just means something shot at something else. It doesn't need its own propulsion and it does not need its own guidance system. A stone from a slingshot counts as a missile by the normal definition.

I'm aware of the etymology. Mitto, mittere. In modern ordnance context, missile = guided, rocket = unguided. Even though both use rocket motors (and here they usually say motor rather than engine).

Balistic missiles aren't really guided. They're closer to the slingshot approach.

But they are guided though, how else would the different warheads be able to have different targets when they are all launched in the same missile.

And is what distinguishes it from a drone the type of flight?

i.e. rocket plus some fins vs wings?

A missile is something that flies through the air with the intention of hitting and damaging a target. The exact mechanism of propulsion is orthogonal to the purpose. A stone from a sling is a missile, as is a pulse-jet-powered drone packed with explosives, as is a quadcopter with a kilo of C4 strapped to it.