The reason why the on-site and off-site prices of index funds are different is that the on-site funds are always in a trading state. If more people buy them, the price of the funds will increase, while the off-site index funds are that investors hand over their funds to fund managers for investment. Besides investing in the index, they may also buy the underlying stocks of the index, so statistics should be made every day after the market closes. Therefore, there is only one off-site fund price every day, and it can only be sold directly at around 9 pm.
Investors can take advantage of the net spread between on-site and off-site funds for arbitrage. For example, if the on-site price is high and the off-site price is low, they can buy off-site and then switch to on-site trading, so there is a price difference.