Every payout option is a trade-off: the more guarantees you ask for, the smaller each check. Think of it like buying insurance on your annuity.
Life only (straight life, pure life): pays for as long as the annuitant lives and stops at death, even if that is next month. No refund. Because the insurer carries the least risk of paying extra, this option gives the highest periodic payment.
Life with period certain (for example, life with 10-year certain): pays for life, but if the annuitant dies early, payments continue to the beneficiary until the certain period ends. The longer the certain period, the smaller the payment.
Life with refund (installment or cash refund): pays for life and guarantees that at least the premium paid comes back; any shortfall goes to the beneficiary.
Joint life and joint and survivor: covers two people (often spouses). Joint life stops at the first death; joint and survivor keeps paying (often a set percentage) to the survivor.
Period certain or fixed amount (annuity certain): pays for a fixed period or until a fixed amount is used up, not tied to how long anyone lives.
Deck mnemonic PRSA: Pure life, Refund and period certain, Single vs. joint, Annuity certain.