The primary cardholder is the main person on the account. They are also known as the borrower.

The secondary cardholder is the co-borrower on the account. One would be considered the primary and the other would be the secondary. Both have equal and full responsibility for the account and full access to all the account management functionality.

Supplementary cardholders are different. They have use of the card for spending only. They're not responsible for the account and don't have access to any account management functionality. A primary and secondary borrower can request supplementary cardholders to be added to the account. One example is a parent adding children as supplementary cardholders to the account. The kids get a card and are able to use it but they are not responsible for payment or account management.