ballistic missiles are big, heavy and expensive. They are basically warheads on a rocket. These missile are launched vertically and only from ground or submarines. These missiles reach heights beyond the atmosphere and then re-enter the atmosphere at the target destination. Their engines switch off after the initial boost and while re entry the missile is accelerated by gravity.
Cruise missiles are smaller, less powerful, lighter and less expensive. They donot exit the atmosphere but rather hug the ground and stay very close to the ground to prevent detection be radars. Their engine remains on at all the time of their path. They are less destructive because of size and weight of warhead. They can be launched from aircraft also.
I hope that explained it.