I'll answer the US bit! A 401K is a tax-deferred retirement plan. Contributions while working come off the top of the member's income, and are not taxed then. Some employers voluntarily supplement these contributions. Interest, dividends, and capital gains accumulate tax-free. When money is taken out, after about age 60, all of it is taxed as current income. How much retirement income depends on the size and timing of the contributions, and market performance over the intervening years, so this type of pension is called Defined Contribution. The old type of pension is Defined Benefit, where the employer or the government guarantees a specific pension amount, and takes the risk of poor performance (or neglecting to make reasonable contributions.)
Another piece of jargon, a 403b, is a similar plan aimed mostly at schoolteachers.
There are several more types of tax-advantaged retirement plans, all luxuriantly festooned with red tape and complex rules, and the UK has its own set.