Apple is indeed using a two-and-a-half year old screen on its brand new iPhone SE. According to the electronics teardown wizards over at iFixit, iPhone 5S and iPhone SE displays are completely interchangeable.
Since it was announced, it's been said that the SE is essentially an iPhone 6S crammed into the body of a 5S, and initial teardowns are showing that is pretty much the case. The SE has the same form factor as the 5S, but it's now clear Apple didn't include 6S features such as 3D Touch and a faster fingerprint reader because it is using literally the same front panel as the older phone, which was released in September 2014.
"The similarities are more than skin deep," iFixit wrote in its teardown of the device. "After a little testing, we found the 5s display is plug-and-play in the SE—fitment, connectors, and functionality are the same. It fires right up."
At $399 base price, the iPhone SE is notably cheaper than any brand new iPhone in recent memory and—this is just a speculation—part of that relatively low price may be because Apple probably had a hell of a lot of old 5S screens laying around from repairing lots of shattered 5S screens. In any case, it's easy to ramp up production of something that's already been designed and perfected rather than to engineer something new.
For would-be iPhone SE buyers, this isn't necessarily a bad thing, if you're cool with the relatively pedestrian screen of the 5S. While it's very difficult to replace only the LCD and screen on the 5S, it's pretty cinchy to replace the entire front panel display, which includes the front facing camera (which is the same as the 5S) and the home button (which is also the same as the 5S).
If you do break your phone's screen, you can buy a cheap replacement from the many, many wholesalers who sell aftermarket parts on eBay and other places around the web. A 5S front display, camera and all, will run you no more than $50, but you can get decidedly less authentic parts for roughly $25 if you shop around. iFixit says its old repair guides will work with the SE, which gives them a little less work to do.
There is one more thing worth noting with the whole this-is-kinda-sorta-an-old-iPhone thing: The Touch ID cable, which connects the home button to the rest of the phone, is a flimsy thing that can easily snap in half while you're removing or replacing the front display. Apple rerouted this cable on the iPhone 6 and 6S, making it substantially easier (and less risky) to repair.
When taking off the screen of a 5S or SE, if you're not super careful, you'll snap that cable in half, which is very bad and will forever break Touch ID on the phone. It's a security feature that makes it impossible for the government or, more likely, a thief, to take the data off your phone using someone else's fingerprint.
Anyways, new phone, old display. That's a good thing if you're clumsy, probably a bad thing if you care about having a phone that looks very pretty.