The definition of the word Pension is......

a regular payment made by the state to people of or above the official retirement age and to some widows and disabled people.

A Pension Plan is where an individual makes payments to a fund that will provide a better income for them in their retirement & they get tax relief on their contributions!
People with a payment plan usually pay a slightly smaller amount to the state pension via NI, so only get the basic pension.
There are many complicated rules, which sometimes change, but if you don't contribute to a private or works pension you will usually get a lower pension.
It was designed to allow the poor in society to have some money to live on in their old age, and I believe that it should be increased to cover inflation.

Those who contributed some of their earnings to a work or private pension plan, just get more because they were, in effect, saving to towards an annuity, so they could have a better life.