An annuity is a payment type which takes the form of monthly installments for a specific period of time, or for the life of the recipient. A pension is a retirement plan in which the benefits are paid as an annuity, so often in common vernacular, they are the same thing.
A pension is the benefit paid from a defined benefit plan. The pension usually comes in the form of an annuity.
The annuities can be paid as single life (for the life of the participant) or joint and survivor (for the life of the participant and then a surviving spouse).
Annuities are not only bought to pay pension benefits, any person can purchase an annuity from an insurance company for any reason. Most often, they are to provide a guaranteed monthly income in retirement or to a child or spouse.
In addition to single life and joint and survivor, there are certain and life annuities. Certain and life are guaranteed for a time, such as 10 years (even if the recipient dies) and then for the remainder of his life.
Annuities, whether from a pension or not, are an excellent way to provide a floor benefit in retirement or to provide income security to a dependent.