Final answer:
Credit cards, debit cards, and smart cards are means of payment that fit in wallets and allow for electronic transactions, while cheques offer a traditional paper-based method. However, only credit and debit cards directly influence banking transactions, with credit cards acting as short term loans.
Step-by-step explanation:
The modes of payment that work through wallets, purses, and card holders are credit cards, debit cards, and cheques. Cash can also be carried in these, but in terms of electronic transactions, it's the cards that are relevant. Credit cards and debit cards are forms of plastic money that allow for money movement without changing the total amount of money in the economy. A credit card provides a short term loan for purchases, paid back when the bill is settled. In contrast, a debit card facilitates immediate money transfer from your bank account to the seller's account, similar to electronic cheques.
Meanwhile, smart cards hold a preloaded value and can be used for specific transactions. They're a convenient alternative, but are limited to the places that accept them. As for cheques, they're physical paper instructions to a bank for payment, which have become less common with the rise of digital payment methods.