Profit- Excess of revenue over expense is known as profit. Profit is what business is left with after deducting such expenses from revenue which made the receipt of revenue doable. It is usually categorized into gross profit or net profit.
Gross profit is the sum of revenue from which trading operating expense has been deducted i.e. expenses related to major actions of the business. Net profit is the sum of revenue that includes incomes from other activities as well and all such expenses has been deducted which were incurred towards major activities as well as other activities.
Gain- Gain is what business earns on selling such assets which is not an inventory of the business. It arises from uneven activities or non-recurring transactions. In other words, a gain is a result of transactions that are minor to the business, other than operating transactions. Here, the sale of the old machinery is an irregular activity; so, the difference is termed as gain Thus, in other words the only difference between profit and gain is that profit is the excess of revenue over expense and gain arises from other than operating transactions. Income includes gain and other earnings like dividends received, interest income etc.