I understand them both as
business, but I am wondering about the difference and nuance and usage.
One question might be why are the big corporations called
대기업 and not
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기업 usually means "groups" which aim to get profit like company, while
사업 means management or business. So, phrases like
그 기업이 하는 사업, which means "The business carried out by the firm", is possible.
Since corporations are groups, "big corporations" is translated as
대사업 is more likely to be "big business".