The difference between a rocket and a missile lies within the means of guidance. Both a rocket and a missile (like all bombs) share many elements in common. The three key elements of all bombs are 1)means of propulsion; 2)the warhead; 3)guidance system; rockets and missiles have 1) and 2), but not 3).
If a bomb does not have a means of guidance, then it is a rocket. a rocket does, however, have a means of propulsion, which makes it greater than a regular bomb dropped from a plane; however, it is still a "dumb" bomb. Unguided rockets are the most commonly used bomb in the world.
If a bomb has a guidance system, then it is a missile. This guidance system could come in a variety of forms, but regardless of "how" the important factor is that a missile can hone in on a specific target, via computer controlled targeting; targeting which uses infrared, radar, or even GPS. The use of a guidance system is what makes a missile a "smart" weapon.