T+0 system means that you can buy or sell futures contracts on the same day, which is different from stocks. For example, if you buy a stock today, you can't sell it until tomorrow. Futures does not have this problem. You can perform multiple operations on the same contract on the same day.
T+0 system and contract month are not the same concept. The target of stock index futures is a futures contract, which has many months. At present, there are four kinds of stock index contracts offered by the exchange, namely, March of the current month, April of the following month, June and September of the last two quarters (the last month of each quarter). Different months represent the delivery time of futures contracts, that is, the time of physical delivery. If you buy a stock index futures and haven't closed your position, then by that month, you need to make up the money to buy a package of stocks (stocks compiled by weight in the Shanghai and Shenzhen 300).
Beginners will definitely have doubts about this, which is basically the most complicated financial derivative launched in China at present. I hope it helps you.