Usually, what you say is right. But, some card, or sometimes, your card will change its agreement. You need to read your card's agreement in order to get that information.

The due day is to avoid "late fee", it has nothing to do with the interests charge (although usually it is the same date). Normally, your interests charge will begin on the day of the transaction, if you do not pay full in the due day. Sometimes, your interets charge will start immediately on the transaction day (this is a "bad" card for us).