You watch the movies on your TV. We have a Roku device we bought a few years back and we get the Amazon or Netflix through that. Some new TV's are "Amazon ready" I guess you could say and then you don't need a device.
Our Prime will be coming up for renewal soon and I will probably renew. We order a lot online and don't always want to wait until we need $49 in merchandise. I also use the Subscribe and Save for paper towels, toilet tissue and even garbage bags. I find it so convenient to get those things in the mail instead of lugging them from the supermarket to home, especially in the winter. You do have to monitor your items though as sometimes the price goes up or they may be shipping before you need something so you can postpone the shipment for another month or two or cancel at any time. I even sometimes buy cereal as strange as it sounds. I recently got 4 boxes of Quaker Instant Oatmeal for less than $2. a box plus free shipping which is far less than the store. I also purchase those boxes of batteries so we always have them on hand. I get the Duracell Pro I think they are and they are far, far cheaper than buying in the store.
Ladydukes, our son gave us a year of Netflix for Christmas so we now have both. I wondered the same thing as you. I think Netflix has a few more things to offer and one big difference is that you never pay extra for anything on Netflix. Many of the movies I checked on Amazon had a charge of $2.99 - $4.99 I think. Even some tv series required payment but there is none of that on Netflix.