The two terms get mixed up constantly, and knowing the difference saves you a lot of confusion when making an animated phone screen.
A Live Photo is an Apple-specific format: a still photo paired with up to 5 seconds of video, stored together in your Photos library. On the lock screen, it animates when you press and hold. Live Photos only exist in the Apple ecosystem — Android phones can't use them, and no website can generate a true Live Photo file (an iOS app like intoLive does the final conversion).
A live wallpaper is any animated phone background. On Android it's usually a short video played by a wallpaper app (or a built-in feature on Samsung and Xiaomi phones). On iPhone, the live wallpaper is a Live Photo set as the lock screen. So: every iPhone live wallpaper is a Live Photo, but "live wallpaper" covers Android too.