Generally Accepted Accounting Principles (GAAP) are based on the accrual accounting system. This means that revenue is recorded when it is earned, and expenses are recorded when they are incurred. No related cash transactions have to occur in order for the journal entries to be made. That difference plays a key role in figuring out the difference between accrued interest and interest income.
Accrued interest could be accrued interest income or accrued interest expense. For accrued interest income, that means that the interest has been earned but no cash has been received. For accrued interest expense, that means that the expense has been incurred but there has been no cash disbursement. For example, a company has a loan and pays interest expense of $300 quarterly that accrues at a rate of $100 per month. After one month, the company would have an accrued interest expense of $100. There would be no associated cash outflow with that $100.
Interest income describes a number of sources of income but usually it is the earnings on a cash balance at a bank. Interest income could also be the interest received on a bond but that is rarer, especially for companies not in the investment business. Earned income does not mean the associated cash transaction already occurred, but that the company earned the interest income. It may mean that the cash was already received, or it may not.
There are two big differences between accrued interest and interest income. First, accrued interest could be an income or expense item that is significant for the income statement. Second, the accrued interest means that the interest was already earned or expensed but no related cash transactions have occurred; while interest income means that the interest was already earned but the cash transaction may or may not have occurred already.
Accruals occur when there is a difference between when cash is earned or expensed and when the accompanying cash transaction is made. Accruals such as interest expense and income are periodic entries and accrue at all times of a day. However, in practice accrual entries occur depending on when the books are updated versus cash transacted. For example, if a company updates its books twice a month and it pays its employees once a month, there will be accrued wage expense. However, if the company updates its books when employees are paid, there will be no accrued entries on the books.