They shouldn't be used perfectly interchangeably, and your professor should be able to explain the distinction, but it still is a messy thing. It was one of semantics in a lot of ways, but official names at given times were consistent. Kevin knows this too, and is probably more consistent than he seems; note that historians of colonialism use "colony" quite freely based on historical relations as opposed to legal names.

That said, the existence of a protectorate requires a treaty with some local ruler or rulers for European suzerainty. It is effectively an arrangement where colonial powers protect their local signatories but take limited roles in local policy (early Uganda fits here, as does early Kenya, when it was the East Africa Protectorate). Protectorate often also signaled a space where colonial claims existed only on paper, but had local treaties that satisfied European legalism. A colony, proper, is a territory that generally contains a lot of conquered territory or people who are ruled under a local administrative regime that is imposed. Sometimes you will hear about a Territory proper, which is a space in some sort of legal limbo, like the mandatory Tanganyika Territory or the Transkeian Territories of South Africa, ruled but not fully incorporated. It can be confusing and contingent, but the big one else to recall is the Protectorate/Colony distinction and the role of colonial presence and power (or local self-rule, and by whom) in each. As for conquered vs. colonized, conquest leads to colonization but is not necessary, and colonization of a key sort happens in protectorate too. The Germans used Schutzgebiet (protectorate) in Südwestafrika (Namibia) and Ostafrika (Tanganyika), though both had regions of European settlement.

Jurgen Osterhammel explains some analytical categories in his book Colonialism: a theoretical overview but these terms are slippery at times when used verbally. Only the legal nomenclature, and context of formation, can really dictate which to use for a given time and territory.

(edit: Hertslett's Map of Africa by Treaty explains some conditions of establishment, and there are a few volumes that give rundowns of name changes over time for various colonizers, usually the British. Stewart, comp., The British Empire is one such.)