Not the same thing. The 18 month option requires an Amazon Prime Rewards credit card. And if you have one of those accounts, great. If not, that involves applying for a new credit card and credit line and the subsequent hard pull on your credit history.
The "5 payments" option is a targeted offer Amazon extends to certain customers (their description uses a lot of weasel words, but I think you need to have been a long-time Amazon customer with no black marks/excessive returns/etc. on your account and a Prime member) where they divide the cost of the item you're buying into five charges across five months to whatever payment method you choose.
It's not a bad option, although it still strikes me as "if you can only afford this item by paying for it a little at a time, then you probably can't afford it period," but that's more philosophical than practical I suppose.