Cheques normally come in small books and you can write the person's or company's name and the amount you pay on one, date and sign it, tear it out of the book and give it to them. They can take it to their bank any deposit it.
Credit cards are plastic cards that you can use to buy things up to a certain limit and then pay in monthly instalments.
Debit cards allow you to pay directly from your bank account without writing cheques- the money is transferred instantly so it's often more convenient than a cheque.
Guarantee cards are used to guarantee a cheque, so that people know they will get their money.