nil rated goods and exempted goods are the same....as the definition of exempt supply says-
“exempt supply” means supply of any goods or services or both which
attracts nil rate of tax or which may be wholly exempt from tax under section 11, or
under section 6 of the Integrated Goods and Services Tax Act, and includes
non-taxable supply;
section 11 of cgst act and 6 of igst act are nothing but gives power to government to exempt any goods/service or any supply in any special circumstances from gst levy on the recommendation of the council.......example of this can be that on 5th August council has recommended to exempt any supply of goods to fifa or any supply of service by and to fifa for fifa under 17 world cup to be held in this month.
hence exempted goods are nil rated goods plus goods notified under section 11/6 of cgst/igst act......
on the other hand 0 rated goods are the goods supplied in the course of export and sold to sez unit or sez developers....hence if any good, whether exempted or not, of exported or sold to sez, becomes 0 rated......
it should be noted that in case of supply of exempted goods no input tax credit is given or refunded to supplier for gst paid on inputs...but in case of 0 rated supply supplier got full it refunded (except block credit)....