Yes they are saying that £100k pension pot will pay you £400 per month - and in fact it's a bit optimistic.
There's something called the 4% rule. If you have a pension which you take as drawdown (ie you keep it invested in the pension, but you take some out each year to live on) then as a rule of thumb you can take out 4% of it each year and reasonably expect it to last you 30 years.
4% of £100k is £333 per month.
The alternative to drawdown is to buy an annuity, which gives a guaranteed income for life. Annuity rates vary, but aten't all that far off the 4% rule.
OP, when you get there you'll want to think carefully about how much of your pension fund to use to buy an annuity, and how much to keep as drawdown, which will allow for uneven income needs over your retirement.
But for now, focus on getting as much into your pension as possible.
Remember that inflation is the killer: if you have it in a savings account with 3% interest but inflation is 5%, then you're actually losing money each month. With your time frame of 20 years, most people would advise investing in the stock market. People have given good advice on where to start learning about how to invest. At it's simplest, you could put pension savings each month into a low fee index tracker in a SIPP.
Be aware of fees - they make a big difference long term.
And look very carefully into terms and conditions before transferring your existing pension. Fees are percentage based (although with a minimum) so it might be doing fine where it is.