I think a 401(k) is a pension? Almost all companies offer a 401(k) for full-time employees.

A 401(K) is not a pension. The latter is funded entirely by the employer.

That's not the case. Pensions are not always funded entirely by employer. In quite a few cases the salary of a worker is reduced by a certain amount that is added to what is contributed towards a pension by an employer.

The difference between a pension and 401(k) type plan is that pension is a defined benefit plan and 401(k) type plan is a defined contribution plan.

Yes, you're right that a pension often involves a reduced salary for the promise of a pension at retirement age. That's a huge part of the appeal of a public sector job that pays significantly less than its counter parts in the private sector. And that's why public sector employees get extremely angry and litigious when governments try to reduce their obligations, even as agencies face dire financial straits.

Which 401(k) plans are you thinking of require paying out to a retired employee if that employee has contributed 0%?

Sorry I'm not following the question.

Why does Wikipedia say it's a pension then?

Because language is imprecise and depends on context - you and the GP are talking past each other. They are using the word in a conversational context and you are using it in an academic/technical sense.

From https://en.wikipedia.org/wiki/Pension:

"A pension is a fund into which a sum of money is added during an employee's employment years and from which payments are drawn to support the person's retirement from work in the form of periodic payments. A pension may be a "defined benefit plan", where a fixed sum is paid regularly to a person, or a "defined contribution plan", under which a fixed sum is invested that then becomes available at retirement age.

The common use of the term pension is to describe the payments a person receives upon retirement, usually under pre-determined legal or contractual terms. A recipient of a retirement pension is known as a pensioner or retiree."

A 401k is a savings account, not a contractual obligation, so that's why it's not a pension in common usage.

You're being willfully obtuse here. No one in the US would call their 401k a pension.

Obviously someone who wrote this Wikipedia article would!

Pension is being used as a term of art here not how anyone uses it in standard parlance.

Not within the context of this discussion. Using your context clues > childish pedantry.