That depends on the context. Revenue is usually the biggest component of gross and net income, although these are accounting terms, revenue is an income in any case. Netting out income and expenses gives you the net income, so it’s probably a bad idea to use net income as it’s synonym.
There are no mistakes, income is the realized inflow of monetary value, that includes all forms of income. Other income here may not mean other comprehensive income (OCI) which are non-operating accumluated gains/loses that are either unrealized, or unqualified to take part of net income such as unrealized P&L’s on available for sale securities (only non-financial firms), currency translations, or changes in the NAV of a defined benefit plan. These are usually included as part of comprehensive income, below the income statement, or on a seperate form.
Other income on the other hand, may refer to income that is part of the company’s earnings, but not part of recurring business operation. Like interest income, rent income, income on equity investments, gain on sale of assets or securities, or asset revaluation (up to the point of previous write-down). Note that a line item other income is usually included in many company’s IS, and it usually an aggregate of non-operating gains and loses net together under other income, or other non-operating income, and can be a negative value. While recurring financial income (interest income, deferred taxes) are included below operating income.
The first one is a more simple equation, and still intuitively correct. It assumes that revenue is your only source of inflow, and cost of goods sold and possibly any fixed assets are expenses. It’s a more simple business model than you can find for bigger public companies.
The other equation is also correct, but it assumes that revenue might not be the only source of income, and includes potentially both operating, and non-operating income.
Don’t get caught up on insignficant details. This is just the beginning of the book. An 8 year old would understand clearly that the money you’re left with is the money you get minus the money you spend. That’s what net income means, and I’m sure you clearly understand the concept as well.
Assuming clean surplus accounting, retained earnings is the amount of earnings you plough back into your capital after distributing cash to shareholders. So RE = NI - Dividends.
OCI are not included in RE. Only the bottom line of the income statement. The second equation is more correct for a public company, since they generally have more than one type of income besides core operating revenue/sales, like investments in other companies, interest income from excess cash investments, or gains on sale of assets or reverse of asset write downs.
The former equation is more common in small business models like a lemonade stand where revenue is your only source of income.
OCI is tranferred directly to equity on the balance sheet and not reflected on the income statement or retained earnings. - includes things like unrealized gains/losess on available for sale securities - actuarial gains/losses on pension obligations
GAINS are transferred through profit/loss on the income statement and through retained earnings. - these are things like gains on sale of fixed assets, or gains - unrealized gains/losses due to foreign currency translation
If you are wondering how unrealized gains/losses arise from foreigh currency translation consider this:
You own a multinational company with a local currency of USD and your fiscal year end is Dec.31. You also operate in China, where this use the Renmimbi, RMB. The current exhxanage rate RMB/USD is 10. You purchase manufactured goods from China on Nov 30 on credit for 100 RMB to be paid on Jan 31, and create an accounts payable for 10 USD (100/10=10). When your fiscal year end rolls around, the RMB/USD is 11. Since you are now able to pay back your debt with less USD ((100/11=9.09), you will have recorded an unrealized gain on the income statement. (10 - 9.09 = 0.91). You will also report your accounts payable as 9.09 USD instead of 10 USD due to the currency appreciation.