It is not. In America, if someone refers to a pension they are usually referring to defined benefit retirement plans, where you work X years and get $Y as a result of some formula and $Y is not related to market performance or how much money is in the pot.

This is significant because the risk is on the employer to make up any short falls if the pension fund is not able to pay $Y because of market performance or underfunding. A 401K shifts the risk to the employee. If it's not enough to provide $Y per year, that's the former employee's problem to deal with.