This video explains the difference between an ordinary annuity and an annuity due.
Both an ordinary annuity and an annuity due are a stream of cash flows; the difference is in the timing of those cash flows. With an annuity due, the first cash flow occurs today. With an ordinary annuity, the first cash flow occurs one period from now.
Thus, the cash flows for an annuity due will begin one period sooner (and will end one period sooner) than the cash flows for an ordinary annuity.
Regarding the formulas, the value of an annuity due is simply the value of the ordinary annuity multiplied by one plus the discount rate.