Two rulebooks answer different questions
Financial reporting aims to describe an entity's financial position and performance under a framework such as US GAAP or IFRS. Tax accounting determines taxable amounts and obligations under a particular jurisdiction's law. A single set of underlying transactions can therefore produce different book income and taxable income without dishonesty.
“Two sets of books” is informal shorthand for reconciled reporting bases, not permission to conceal records. Companies often maintain one transaction system with schedules and adjustments that support multiple purposes. Audited public-company book reporting and a tax return need not use the same depreciation, recognition timing or deductible expense rules.
A shared machine, two schedules
A machine costs $100 and has $20 book depreciation this year. Suppose a hypothetical tax rule permits a $40 current deduction. Book profit includes $20 expense; taxable profit includes $40 deduction. Current taxable income is $20 lower than book income from this difference, with future consequences when the schedules reverse.
Cash versus accrual is another dimension. Tax law may permit or require particular accounting methods depending on the taxpayer, activity and conditions. It is incorrect to assume all tax returns use cash accounting or that every private business follows one public-company book model.
Keep four amounts distinct: book pretax income, taxable income, current tax expense or payable, and cash tax paid. Payments include installments, prior-period balances and refunds, so cash paid need not equal the current-year tax expense.