Offline Debit Card

What Does Offline Debit Card Mean?
A card that combines characteristics of both a traditional (online) debit card and a credit card, allowing the cardholder to pay for goods and services directly from his or her bank account. As with a traditional debit card, a transaction using the offline debit card creates a debit against the cardholder's bank account. But unlike with a traditional debit card, no PIN is required during the transaction - all that is required is the user's signature. These cards are generally issued by credit card companies in association with the bank in which the account is held.

Also known as "check cards".

Investopedia explains Offline Debit Card
This type of card will often have a maximum daily limit. If this is not the case, the maximum amount is based on the funds held in the underlying bank account. Because this debit card is "offline", the bank account is not accessed directly, meaning there's a delay of 24 to 72 hours before the amount of a purchase is debited from the account.