Yeah, buying points is a bit different though and again is a great example of why everyone should at least have a basic understanding of how to make an amortization schedule.
Buying points isn't exactly the same as a higher down payment, because that money doesn't take any principal off your loan. It's basically paying interest up front, giving the lender a lesser amount now rather than a greater amount later.
Shit gets complicated real quick, so plugging it into an Excel spreadsheet makes it much more clear.