A ballistic missile is targeted as a projectile from a single launch force with not much added guidance. Higher range ballistic missiles are generally launched directly into the high layers of the earth's atmosphere. It travels well outside the atmosphere and then the warhead detaches and falls back to earth. It follows the path of a ball thrown upwards which falls down.
Example: Prithivi, Agni Series Missiles from India
Where as a cruise missile cruises, over land or over water. Its working is similar to a jet engine powered airplane. Cruise missiles are either subsonic or supersonic depending on their propulsion and design. It is generally guided and use engine on all the flight path.
Example: Brahmos Missile, Tomhalk Missile