Though both the words underline suppression of the other, Colonialism is where one nation assumes control over the other and Imperialism refers to political or economic control, either formally or informally. In simple words, colonialism can be thought to be a practice and imperialism as the idea driving the practice.
Colonialism is a term where a country conquers and rules over other regions. It means exploiting the resources of the conquered country for the benefit of the conqueror. Imperialism means creating an empire, expanding into the neighbouring regions and expanding its dominance far.
Colonialism is termed as building and maintaining colonies in one territory by people from another territory. Colonialism can altogether alter the social structure, physical structure and economics of a region. It is quite normal that in the long run, the traits of the conqueror are inherited by the conquered.
Colonialism is a term used to describe the settlement of places like India, Australia, North America, Algeria, New Zealand and Brazil, which were all controlled by the Europeans. Imperialism, on the other hand is described where a foreign government governs a territory without significant settlement. The scramble for Africa in the late 19th century and the American domination of Puerto Rico and the Philippines can be cited as examples of Imperialism.
In Colonialism, one can see great movement of people to the new territory and living as permanent settlers. Though they lead the life as permanent settlers, they still maintain allegiance to their mother country. Imperialism is just exercising power over the conquered regions either through sovereignty or indirect mechanisms of control.