Otherwise
Part of speech: adverb
Definition: Differently, in another way. In different circumstances. In all other respects.
Part of speech: adjective
Definition: Other than supposed, different.
Example sentence: A house must be built on solid foundations if it is to last. The same principle applies to man, otherwise he too will sink back into the soft ground and becomes swallowed up by the world of illusion.
Differently
Part of speech: adverb
Definition: In a different way.
Example sentence: The people made worse off by slavery were those who were enslaved. Their descendants would have been worse off today if born in Africa instead of America. Put differently, the terrible fate of their ancestors benefitted them.