
SS is a defined benefit administered (and guaranteed) by an independent agent. Pension is a defined benefit administered by employer (or PBGC). Seems pretty similar to me.
Annuity is a defined contribution disbursed formulaically by a company you hired. The only similarity is the regular payment.
The main difference is who bears the risk. For pensions, it’s the employer, who has to make extra payments if the pension fund falls behind it projected obligations, or surrender its management to PBGC. That open-ended risk is why most companies have abandoned pensions. For SS, it’s the government (although they do have the power to change their legal obligation). For annuities, it’s the recipient, who will just get less money if the annuity’s investments underperform during the accumulation phase.