I would say that the cash dispenser is the PART of the ATM machine that actually dispenses the cash.
In our supermarket, there are "self-checkout" machines where you scan and bag your groceries yourself. Often you pay with a credit or debit card, and you have the option of getting a small amount of cash back--you can buy $32 worth of groceries, ask for $10 cash back, and have $42 charged to your card. The $10 is dispensed by the machine. Thus, this machine is NOT an ATM machine, but, like an ATM machine, it HAS a cash dispenser.