In the US (Yes it can depend on region), photo caching is typically on by default when using the official DJI Fly app. It's not offered in third party apps such as Litchi for example. Video caching can be turned off or on in the menu (found it to by on by default).
The copy saved to the phone is usually a lower quality/resolution than the copy that gets saved to the SD card.
In some countries such as India due to local laws/restrictions, the photos are saved strictly to the SD card with no image cache to phone option capable.