Nil rated supply and exempted supply

Goods or services on which GST rate of 0% is applicable - Nil rated

Exempt supply includes nil rate supplies, non-taxable supplies and specific supplies which are notified as exempt from tax. 

GST rate 0% - nil rated

Excempt as per GST act - Excempt Supply

Exempted supply are those GST is not applicable . ---We cant claim ITC

For Nil rated items GST applicable at 0% and the amount payable is nil –We can claim ITC

As per SECTION 2 (47) of the CGST Act 2017,

"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.

Whereas, NIL rated Goods means they are 0% rated Goods or Services.

Nil Rated It is the supply of goods and services that have 0% GST.
Example: Grains, salt, jaggery etc.
Exempted It is the supply of goods and services that does not attract GST and allows no claim on ITC.
Example: Bread, fresh fruits, fresh milk and curd etc.

Items exempt from GST are the commodities that have not been included in GST yet.

Nil-rated items are the items which are included in GST and have been put in the 0% tax slab.