In Canada you can opt to receive your CPP (Canada Pension Plan) at anytime between 60 and 65 or as late as 70.
There is a number called YMPE (Yearly Max Pensionable Earnings) that is approximately the average industrial wage. CPP is calculated as the average of how much you contributed every year you worked except the worst 7. The pension is then based on that proportion - currently the YMPE is about $60,000 a year and the max annual CPP about $13,800 a year. People with a decent income typically make more than the YMPE most of their life and collect the maximum. If you choose to retire before 65, the amount you collect goes down by 0.6% each month (7.2% per year) for each month before 65. So if you retire at age 60, your CPP amount is 36% lower than what you would have gotten at 65. (You can also delay collecting until later, up to age 70, and your payout will increase by 0.7%/month when you do start.)
Like another thread here about social security - early pension makes sense if you have severe medical problems and probably don’t need an independent living income in your 80’s and 90’s, since the break-even n total income is late 70’s.
There is also an old age supplement that starts at 65. Note all this is taxable income. If you have a large amount of savings, one strategy may be to delay the CPP (and then get a bigger payout, later) while drawing down your savings instead. Depending on total income, this may reduce the amount of income that falls into higher tax brackets.
Defined benefit pensions plans and early retirement pension plans are a dying breed in North America. Typically only governmental organizations (civil servants, army, police, teachers, etc.) and large heavily unionized industries are the ones that offer them. Some offer 30 years and out which could allow retirement at 48. Most have something like “rule of 80” or “rule of 85” - when your age and years of service total 80 (or 85) then you can retire on a full pension, typically calculated as a percentage of the best 5 of your last 10 years wages.
Many early retirement pension plans offer a higher “bridging amount” until you reach 65, when they assume your CPP will commence and supplement your regular pension. They are forbidden from explicitly subtracting the CPP amount, but they use math tricks to estimate it. The value of this rule, I assume, is that the calculation cannot change after retirement - if the CPP becomes inordinately higher that does not then reduce the amount the pension plan can pay to already existing retirees.
I have heard of pension plans that allow “buying extra years” as the OP mentions (but not government plans), and particularly there are those that allow re-buying: a person is laid off or quits, and takes their pension as a lump sum to manage themselves; then rejoins the company and wants to re-acquire credit for their years they had in the plan - they can buy back their previous “years” by paying back in the “net present value” of that pension credit.