Notes receivable and accounts receivable both show up on your balance sheet as assets. Accounts receivable tracks money you're owed but haven't received yet. Notes receivable does too, but this category only includes debts that have a promissory note attached. Debts entered as notes receivable are usually paid back over a longer period.
Suppose your firm delivers $2,000 of ball-bearings to a customer. If they're not paying up front, you present them with an invoice, then enter the $2,000 owed in your business records. Unless you're running your business strictly on a cash basis, you count the $2,000 as income once you deliver the ball bearings. When you update your balance sheet, you take the total amount your customers owe you and record it as accounts receivable. Just as the $2,000 counted as income, on the balance sheet you treat it as an asset.
Debts included in accounts receivable are usually short-term with payment due in 30 days or less. There may be nothing in writing besides your invoice, but you're still entitled to payment once you deliver the goods. If the client wants to pay over a longer period, or you're not sure they're trustworthy, you might prefer to confirm the debt with a promissory note.
A promissory note is a written IOU. Suppose you contract for a $30,000 remodeling job, but the customer can't pay you for six months. You require they sign a promissory note saying "I, John Q. Customer, owe $15,000 due six months from this date." Usually, the note sets an interest rate too. Written properly, the note is legally binding. It's also "negotiable," for example, if you sell or give the note to someone else, they have the same claim on John Q.'s money that you do.
If a customer has trouble paying their accounts receivable bill, some businesses will offer more time to pay, in return for signing a promissory note setting out the new terms.
If your customers owe debts that have promissory notes attached, you record the debts under notes receivable. This goes on the balance sheet separately from accounts receivable, though it still counts as an asset. Suppose your customer is two months late paying a $1,100 bill. You offer three months extra time to pay, in return for a promissory note, and the customer agrees. You subtract the $1,100 from accounts receivable and enter it into notes receivable.
Accounts receivable goes on the books as a current asset. You do the same for the portion of notes receivable you expect will be settled in the next year. The money you'll receive more than 12 months out goes on the books as a non-current asset.