Otherwise means if not, or in other circumstances. Hurry, otherwise we'll be late, otherwise excellent, think otherwise.
It does three jobs: naming the consequence of not doing something, meaning in other respects — otherwise excellent — and meaning differently, as in think otherwise. Otherwise engaged is a polite refusal. Note that the word is other plus wise in the old sense of manner, the same wise as in likewise and clockwise.
1adverbotherwiseIf not; or else.
“Wear a coat, otherwise you'll get cold.”
2adverbrespectsIn other respects.
“The soup was a bit salty, but otherwise the meal was excellent.”
Too few real examples of this word to estimate which sense is commonest.
otherwise is a connecting word.
Old English on othre wisan means in another manner. The wise here means manner, as in likewise and clockwise.
Old English
on ōþre wīsan
Middle English
otherwise
English, today
otherwise
From Middle English otherwise, othre wise, from Old English on ōþre wīsan literally “in (on) other/different manner”; equivalent to other + wise. Compare West Frisian yn oarwei (“otherwise”), Icelandic öðruvísi (“different”).
Etymology from Wiktionary, CC BY-SA