In modern military usage the term "missile" refers to a self-propelled guided weapon system, while a self-propelled unguided weapon system is referred to as a "rocket." For a "rocket" the propulsion system is typically a rocket engine, while for a "missile" it can be a rocket engine, jet engine , and/or another means of self-propulsion. A rocket engine does not require outside oxygen and so anything leaving the atmosphere, such as an Intercontinental Ballistic Missile (ICBM), would use a rocket engine. A cruise missile that would travel long distances and stay within the atmosphere would more likely use a jet engine instead, as it would not need to carry oxygen for the engine. Rocket Motors (solid-fuel rocket engines) are frequently used for these weapons due to their reliability, ease of storage, and ease of handling.
Nobody here but us chickens!