How are cruise missiles different from ballistic missiles?
A cruise missile is rocket or jet powered and flies to its target within the atmosphere, using lift to stay up. Most have wings, although a few may use lifting body designs. They maneuver using control surfaces on the wings and tail like an airplane. Mission profiles can include big course changes, to evade air defenses, or to hug terrain to stay hidden. They can be launched from fixed ground positions but most are launched from mobile platforms. They tend to have shorter ranges than ballistic missiles. 

A ballistic missile is a rocket that powers its way out of the atmosphere and coasts in an arc, re-entering the atmosphere before hitting its target. They have little maneuvering capability, once the boost phase is done it's all down to physics. Some warheads are able to maneuver a bit in re-entry in order to hit a pinpoint target, others are just rocks at that point. The largest ones are launched from fixed positions like missile silos but smaller ones are mobile.