In the UK, they refer to defined contribution and defined benefit as pension.
In the US, pension is short for “defined benefit” pension, which is an annuity beginning at a specified retirement age. The liability for providing that benefit does not lie with the recipient of the defined benefit, but with the employer (or government).
A defined contribution pension is one where the recipient of the benefit owns and controls the assets that will be used to pay the retirement benefits, hence the recipient is liable for making sure to have sufficient savings and the right investments to be able to pay themselves in retirement.
In the US, social security is the defined benefit pension available to everyone provided by the federal government.
However, it is prudent to expect defined benefit pensions to decrease in value as the retirement ages are increased, and benefit amounts and future value of money are decreased due to slowing economic growth in most developed countries.
Yes, a 401k is one type of DC pension. Specifically, one subject to various stipulations of the tax code section 401(k), where an employer has to setup the plan in such a way that sufficient employees benefit from it in sufficient amounts to pass the non discrimination testing. In exchange, the income contributed is not taxed until it is withdrawn after retirement age.
A Roth 401k is the opposite, where the income contributed is taxed today, but the withdrawals are not taxed after retirement age (unless politicians change their mind in the future...)
An IRA (individual retirement account) is similar to a 401k, except it involves no employer, and the amount of income that can be contributed pre tax is much less, and maybe zero if you earn too much in a year.