Two choices, the same money: each tool shows what both would leave under the assumptions you enter.
Two ways to use the same money: buying a home or renting a similar one, and keeping money in a savings account or investing it. Each tool shows what both choices would leave under the assumptions you enter.
No. They compare modeled money only. Things a calculator can't weigh, such as stability, flexibility or how quickly the money can be reached, are left to you.
Both tools hold the rates you enter constant every year, and small differences add up over many years. Each page has a table showing how the result changes when the main rates change.
Yes. Each calculator page has a section on how the result is calculated, and a link that reopens the page with the inputs behind the example result, so you can reproduce it by hand or in the tool.