This is a great question. There will be debate, because definitions are very difficult to come by. One way to look at the relationship between colonialism and imperialism is to view imperialism as the ideology that propels colonialism to take place. Let me parse this out a bit.
Imperialism is the establishment of unequal economic and social relationship between people who have power and people who do not have power. Imperialistic nations of the past have included: Rome, Persia, and more recently various European nations. Colonialism is one of the chief ways a country exercises their imperialistic designs.
Not all will agree with this definition. For example, Edward Said does not see colonialism in this way at all. He sees colonialism as a commercial endeavor of one people in another area. Of course, this colonialism can have imperialistic designs, but does not necessarily have to.
In my opinion, the two words are related. More times than not a colony will exploit that area for the benefit of the colonizers. This, in turn, is imperialistic.