Are the payment of ex-gratia and payment of statutory bonus the same under the Payment of Bonus Act, 1965?

No, they’re different. 
Statutory bonus: Mandatory under Payment of Bonus Act, 1965 (8.33%–20%).
Ex-gratia: Voluntary, outside the Act, paid at employer’s discretion. 

Shekar Ganagaluru's Books

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K. VITTALA RAO's HR Books