A charge card must be paid in full every month. Unlike credit cards, there is no option to revolve a balance, or to carry a balance from one month to the next. Anything less than payment of the balance in full each month, and the cardholder is considered delinquent.
Amex's traditional credit product is charge cards. Today, however, they offer charge cards and credit cards both.
Amex charge cards do not have a credit limit in the same sense that a credit card does. They are advertised as having no preset spending limit, although they do place an internal limit on your monthly spending that changes from month to month, and is based on your monthly spending patterns and payment history with Amex.
Because of their history in the charge card business and their overall skittishness in general, it is advisable to treat any Amex credit product as a PIF-type card. Even if you have a card that allows you to carry a balance, they really hate it when you do, and have been known to get nervous and close accounts or lower limits on credit cardholders who carry a balance for more than a few months at a time.