Banks generate income through different product and services like one of the primary ways is by lending money to customers at a higher interest rate than the rate at which they borrow money from other banks or the central bank. The difference in interest rates, known as interest rate spread allows banks to earn a profit on the loans they make. Banks also charge fees for various services such as account maintenance, ATM usage and wire transfer. Banks may invest their own funds in various financial instruments such as stocks, bonds and real estate to earn a profit on their investment. Some banks generate income by providing advisory services to clients or by offering insurance products.
Although the information you have given varies between countries but it is partially correct. The sources from which banks provide the largest flow of funds and money generally consist of savings provided by clients. In addition other options with high income are provided from the commissions obtained from the service fees offered as well as the income from the investments as you mentioned. Finally, considering that banks operate in the service sector, can you explain what you mean by the "product"?