To begin with, both of them are adverbs, "otherwise" can be an adjective but they are NOT the same.
OTHERWISE -> in other respects or ways, in another and different manner, other than expected
for example: "I was guessing that you didn't understand but it was otherwise."
On the other hand, "vice versa" doesn't refer about another idea, manner or possibility. It refers about the reverse or the other way around.
VICE VERSA -> (adv.) with the order reversed
for example: "My mother loves my father and vice versa."
Vice versa in this sentence means reverse. In that case, the reverse of "my mother loves my father" is "my father loves my mother". Instead of writing the whole sentence, we use vice versa.
If i use otherwise in the previous example, it would mean that my mother loves my father and she also hates my father because otherwise here is referring to the opposite and NOT reverse.
