Depends on the locality. In the UK, they refer to something similar to 401k as a pension also. The long form would be “defined benefit pension” or “defined contribution pension”.

In the former, you are promised (defined) how much you will get in your retirement, in the latter, you are promised how much will be contributed to your retirement savings (but not how much you will get).

> The nitpick about how much the manager shows how much you've been fooled.

I do not know what this is referring to.

>Elsewhere, a pension is a government guaranteed faucet of money for retirement.

The US has that too, called social security.