In the US, pension is short for “defined benefit pension”, most often a provided by a single employer stipulating that you work at that employer for a minimum number of years, and the longer you work at one employer, the greater the benefit.
They only exist at taxpayer funded employers or legacy businesses like oil and gas, but most everyone else has switched to defined contribution pensions, but those are referred to as “401k” or “401b” or some other letter for the appropriate section of the law that specifies the tax benefit of saving for retirement.
The latter are better ever since low cost index funds came about, as you get to skip paying the DB pension administrators and remove agency risk.
Virtually all people who have worked and retired at oil and gas companies over the past 40 years had both a company pension AND a 401K. My dad has a paid off house and no bills other than utilities and taxes. He's pulling in over 80K a year in retirement, and he re-invests most of what he's being forced to pull out.