Looking purely at the translation, I don't think you can - at least given the situation here. 'Non-profit' and 'Public good' are two completely different things. For instance - it is quite common here to have clubs, such as sports clubs, and social clubs. A club is NOT a bar, although it can be. The club does not make a profit. But it operates for the benefit of the members of the club, not for public good. Sure - there are also many associations that are for public benefit, and which are non-profit. Being one thing does not make it both.

Are you asking Chinese or English speakers? Google Translate translates both of your phrases the same, so I think they might be equivalent, but I'm not a Chinese expert. Peruse the links on this search result. You will see both of your phrases in use. Can you determine from this if they are equivalent? https://search.yahoo.com/yhs/search?p=%E5%85%AC%E7%9B%8A%E7%BB%84%E7%BB%87+english+non-profit+&ei=UTF-8&hspart=mozilla&hsimp=yhs-001