The discrepancy between gifts and this field is due to a failed payment on a recurring gift. For example, if a payment failed in April but a payment was successful in May, the "Paid Through" field would still reflect April. You can see further evidence of this by looking at the "Balance" and the difference between the "Total Committed Amount" and "Amount Received" fields. If the gift has failed a payment, the "Amount Received" will be lower than the "Total Committed Amount".
To resolve this, you must create a Forgiveness on the recurring gift which will update the "Paid Through" field once the next gift is made. Otherwise, you will continue to see an inaccurate "Paid Through" date.