Continuous in the current month means that all contracts in the latest month (not the current month) are continuous, because the price change varies with the distance between contract months.

The "continuous month" here is not a fixed month, but always changes. For example, today is July 2 1, and taking corn futures as an example, then "continuous month" is C2008. If the delivery date in August 2020 is passed, then "continuous in the same month" becomes C2009 again.