How is using the SANDMARC Telephoto Lens different from using the iPhone native telephoto camera?
The short answer is: better optics and further zoom.
The long answer? The iPhone's wide camera is superior to the iPhone's Telephoto camera, in terms of picture quality - especially for subjects more than 8 feet away. The sensor is slightly larger (1/3" vs. 1/3.4"), and the pixel size is larger (1.22µm vs. 1.0µm).
Therefore, when using the SANDMARC Telephoto Lens on the iPhone Wide Camera, you are able to achieve the zoomed in telephoto frame while still using the iPhone's best camera. To achieve the telephoto frame without the SANDMARC Telephoto Lens, you would either have to use the iPhone Telephoto Camera (which doesn't photograph subjects well that aren't within 8 feet), or you would have to use digital zoom with the iPhone Wide Camera, and digital zoom results in reduced picture quality.