Thanks for your question
PAYE ensures (as you have established) that tax is deducted each time you receive a payment, whereas incomes on which PAYE cannot be operated on, such as rental income, investment income and self employment, has to be reported on a self assessment tax return.
If an individual has to fill in a self assessment return then they declare ALL income, and if there has been PAYE income such as employment, then this would include the income earned and the tax deducted, and non PAYE income on which no tax has been deducted.
The reason ALL income is declared is because for tax purposes, you only have a entitlement to one set of personal allowances (The £8105) and as this has already been used against the PAYE income, if you did not include PAYE income in the self assessment return then the calculation of tax due, would offer another set of personal allowances, and also not take into account, whether combined incomes for the year, saw an individual liable to a higher rate of tax (as annual income of more than £42475 sees 40% tax being due on excess income, and then if an individuals income is more than £150,000 then excess income at 50% tax)
Si in essence if your PAYE income and your rental income is less than £42475 =- then yes, its the same as if you are just charged 20% on the rental income, but only through the fact that the WHOLE income position has been reviewed.
So self assessment just brings all income for the year into one streamlined review for HMRC to ensure the right tax is paid.