A return without a time attached is half an answer
Return on investment is the simplest measure in finance: what you got back, less what you put in, over what you put in. It is also the most quoted measure without the one piece of context that makes it mean anything. The same return is excellent over a year and mediocre over a decade, and the difference is not a detail.
That is why this page prints two figures. The plain return is what most people mean by ROI and what most sources quote. The annualised figure underneath it is the rate at which the money would have had to grow, every year, to get from the first amount to the second in the time it actually took. Comparing two investments means comparing the second figure.
Nominal a year, and effective a year
The annualised return appears twice, in two conventions, because both are in common use and they are not the same number. The first is a nominal annual rate on a monthly grid: the monthly rate multiplied by twelve, which is how a lender or a bond desk quotes. The second is the effective annual rate: what the same growth comes to when it is compounded once a year, which is how a savings account has to be advertised in most places.
The effective figure is always the larger of the two when the return is positive, because compounding within the year is being counted. Neither is wrong and neither is a rounding of the other. Quoting one where the other is expected is how two honest sources end up disagreeing about the same investment.
What the calculation leaves out
It takes two amounts and a length of time, so anything that happened in between has to be folded into one of them. Dividends, rent, coupons and any other income count as part of what came back, on the assumption that they arrived at the end; if they arrived early and were reinvested, the true return is higher than this page reports. Money added part way through is not something two amounts can express at all, and the IRR page is the one that takes a stream of dates and amounts.
Tax, dealing fees and inflation are all absent. A return after tax and after inflation is a different and usually much smaller number, and turning this page's answer into that one needs figures this page never asks for.