I have to define "colony," "protectorate," "sphere of influence," and "economic imperialism" (related to imperialism), but I can't find any information.
All of these terms that you mention have to do with imperialism. They are different ways in which one country can exert imperial control (or some degree thereof) over another. As you have them listed in the question, the first three go from the one where the imperial power has the most control (colony) to the one where it has the least (spheres of influence).
A colony is a country that is completely controlled by another country. The imperial power actually takes official control over the colony. Some people from the imperial power generally come to live in the colony. Australia was once a colony of Great Britain. India was a colony as well, though many fewer Britons went to India than to Australia.
A protectorate is...
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