When talking about pensions in the USA, people are usually referring to retirement plans where the employer says something roughly like "when you retire, we will pay 80% of your salary". or "when you retire, we will pay you X/month". The responsibility is on the employer to ensure that money is around when you retire.

Companies used to have things like this - when my dad retired he had several pensions from multiple companies that worked like this. Nowadays government usually uses them to put off paying the full cost of employees.