There are several synonyms that can be used for the term "discount card". One of the most commonly used is "loyalty card", which refers to a card that is used to reward customers for their loyalty and patronage. Another synonym for "discount card" is "membership card", which is used to provide discounts to members of a specific organization or group. "Shopping card" is also a synonym for "discount card", as it is a card that can be used to gain discounts and other savings when shopping at certain retailers. Finally, "promotional card" is another synonym that can be used to describe a card that is used to promote a brand or product, typically through providing discounts and other promotional offers.