A Federal Court fight between Taronga Zoo in leafy Mosman and a proposed second zoo in Blacktown is about whether "western Sydney is in Sydney", the court has heard.

Taronga Zoo, on the shores of Sydney Harbour, is suing the company behind a proposed $36 million cage-free zoo in the Western Sydney Parklands at Bungarribee to stop it using the name Sydney Zoo on a number of grounds, including that it is not in "central Sydney".

It has launched two separate but related Federal Court cases: the first to prevent Sydney Zoo registering the name as a trademark and the second to have the court declare the use of the name would constitute misleading and deceptive conduct.

The not-for-profit Taronga says the name is likely to lead visitors into the "erroneous belief" Sydney Zoo is the "long-established and well-known" Taronga Zoo and is "located in central Sydney" rather than 33 kilometres west of the CBD.