The university defended the guidelines, insisting it was not mandatory for students to use the language.
"It uses a more appropriate, less appropriate format," a UNSW spokesperson told the BBC.
"The guide suggests referring to Captain Cook as the first Englishman to map the continent's East Coast is 'more appropriate' than referring to his 'discovery' of Australia."
The guide also suggests using the terms "Indigenous Australian people" or "Aboriginal peoples" instead of "Aborigines" or "the Aboriginal people", to avoid suggesting all Indigenous Australians are the same.
It says using the term "complex and diverse societies" is more appropriate than using words such as "primitive", "simple", "native" and "prehistoric".
The guidelines also sparked a heated debate in social media.
One Twitter user, Bernard Gaynor, said: "More PC rubbish. Now the University of NSW is telling us that Captain Cook invaded Australia." Another, Osman Faruqi, tweeted: "About time.
How can it be controversial to no longer refer to Cook as the guy who 'discovered' Australia."