the difference in the greeks is when comparing different trading platforms. e.g ToS, IB, TS, etc... same strike, expiry, etc... the only difference being the trading platform that is providing the greek (delta, theta, etc...). I don't think I will get the answer as to the formula they use. eg the IB reps don't seem to know.They are basically the same, since they move the same... both are on SP500.
Difference in some greeks would be due to difference in maturity... difference in American vs European... difference in dividend dates. Possibly some difference in interest rate, since ETF rate is involved.
IV should be the same, since the underlying vol is basically the same...
thanks for your comments on spx vs spy. Bob mentioned something about spx is tied ES futures... hadn't heard of that before. I would have thought they would be tied to SPX. SPX is the 'ground zero' of the index afterall...