Live Photos are animated photos, not videos.
What makes it confusing is the difference between creative semantics and technical semantics.
Technically speaking, Live Photos is both a photo and a video. The media that is created is a photo JPEG and a QuickTime movie. But that is not really important. That is just an implementation detail. In a future implementation, Live Photos may be only photos-based — it may just be a succession of JPEG photos that were taken 30 per second.
But creatively speaking, Live Photos is an animated photo, not a video. The user has decided to capture a still photo — as opposed to deciding to make a short movie — and they have composed a still photo in their viewfinder as always, and pressed the shutter once to capture that one single moment. They are not going through the process of shooting a movie where you press Record and frame a shot and move the camera around to communicate a narrative and ultimately press Stop. They have taken a still photo with a single shutter press in the same way they have done for over 100 years. However, with Live Photos, instead of the still camera capturing only a still photo, it has captured a few moments before the still photo and a few moments after the still photo to create a loop that brings the photo to life. Creatively, that loop is not a video — it is an animation.
This concept did not originate with the iPhone. It has been done for years by pro photographers, and it has been featured in many works of fiction. For example, there are “magic photos” in the fictional Harry Potter stories. An otherwise unremarkable still photo frame shows a short loop of the moment that was captured rather than just a still photo. But semantically, that is still a photo. It is just an animated photo. There is no narrative as in a movie.