Both Cheque and Expense report a transaction as an expense and a payment simultaneously.
While Bills are for payables (received services or items to be paid later) Cheque and Expenses are for services or items paid on-the-spot.
If you need to print a check, record an expense as a Cheque, instead of an Expense.
If you paid something via credit card, use Expense.
If you paid something via EFT, you should still use Cheque or Expense. You can enter EFT in cheque number field.
As an example, if you bought supplies at Office Depot and immediately paid for them, record the transaction using Cheque or Expense. You can skip entering and paying bills, because there's no money owed to Office Depot.