Why is there a difference between NSE's IV and Rupeezy's IV?

The implied volatility (IV) on Rupeezy differs from NSE's because the two are calculated differently. NSE uses its own fixed assumptions: it computes IV at fixed intervals from each option's last traded price and the underlying's value, applying a benchmark interest rate. Because the call and the put are worked out separately, NSE can show two different IVs for them even at an at-the-money (ATM) strike, where they should be the same.

Why are NSE's IVs for in-the-money options lower?

Illiquidity and the Securities Transaction Tax (STT) on in-the-money (ITM) options push the volatility of ITM options down further.

Rupeezy instead uses a single IV for the call and the put at the same strike and expiry — see Why is there a single IV for Call and Put options?

Things to keep in mind