Quote from 1245:
I understand that. If you are trading IWM, the ETF, the options are priced off the ETF. If you are trading the RUT, the cash settled index, the market makers price the options off the last sale of the Russell future that best covers the option expiration. There is a big difference between the last sale of the Russell cash index and the last sale of the future. In calculating the Ivol, this would cause a difference.
1245
To be correct they price options off the last sale of the Russell future that best covers the option expiration + base offset. You always price your options/greeks off ATMF (at-the-money-forward) price, it's just how you arrive at this price is different. So future price + base offset is just one of the models.
Also there're different flavours of delta like gamma-adjusted delta (useful for delta-hedging), skew adjusted delta (or skew-delta, useful for vol trading). It may be that TOS publishes raw BS delta while OptionVue publishes gamma-adjusted delta.