Not quite - there's two aspects to Apple Pay (which is why many people get confused over whether retailers support it or not).
First, there's the simple replacement for non-authenticated payments of <£20 which is pretty much the same as contactless cards or what other RFID phones can already do, with the difference that Apple Pay doesn't provide the card reader with your card number, instead it provides a single-use number. Not sure if other phone's systems do that. There's no special terminal or support needed for this - if a retailer can take contactless payments, then your can use Apple Pay, the reader just sees it as a contactless card.
The other aspect of Apple Pay is that for larger transactions (over the £20 limit), users can authenticate on their phones (with fingerprint or passcode) rather than using a PIN, and again the retailer and the payment processor will never actually see your credit card number, just the one-time number transmitted by your iPhone. This is going to need specific support, hence the list of retailers who "support Apple Pay".
I'm sure someone can give a more technical explanation than that, but the bottom line is you never provide your actual card details. So effectively Apple Pay is an anonymising service for card payments with the associated security/privacy benefits that brings about.