Why tax-free NRE is only half the story
In India, interest on an NRE account is exempt under Section 10(4), for as long as you hold the status of a person resident outside India. India charges no tax and the bank deducts no TDS, which is where the tax-free reputation comes from. That reputation is accurate, but only inside India.
Australia taxes its residents on their worldwide income, and it does not recognise India's NRE exemption. So the NRE interest is ordinary assessable income on your Australian return, taxed at your Australian rates in full. And here is the sting: the foreign income tax offset only credits foreign tax you actually paid, and on NRE interest India took nothing, so there is no offset at all. The result is that tax-free NRE interest is taxed in full in Australia, with nothing to soften it. Many people carry large NRE balances assuming the interest is genuinely tax-free and are caught out when their Australian accountant adds it in.
NRO interest works differently
NRO interest is taxable in India. The bank deducts TDS under Section 195 at 30% plus surcharge and cess, but the India-Australia treaty caps the tax on interest at 15%, and you get that lower rate by lodging a tax residency certificate and Form 10F with the bank before the interest is paid. If you do not, the bank deducts the full 30% and you are left recovering the difference.
On the Australian side, the NRO interest is assessable too, but because India did tax it, you get a foreign income tax offset for the India tax. The important detail is that the offset is limited to the tax correctly payable under the treaty, that is 15%. So if the bank over-deducted at 30% because you had not lodged Form 10F, Australia will still only credit 15%, and the extra 15% has to be reclaimed from India by filing an Indian return, not from the Australian tax office. Lodging the Form 10F up front is what keeps the two sides aligned.