Conversely = On the contrary. It's used when the two things being compared are opposite. e.g. I like football. Conversely, my wife hates football. "In contrast" (no "the") is for this kind of contrast. e.g. I like coffee. In contrast, my wife likes tea. Tea and coffee are not opposites but different. Use "conversely" and "in contrast" in formal situations, not like my examples!