Factory Testing is a kind of sanity check on mobile devices. It's conducted automatically to verify that there are no defects brought by the manufacturing or assembling.
Mobile Testing contains
Mobile application testing Hardware testing
Protocol testing mobile games Testing Mobile software compatibility Testing.
Certification Testing is the check before a mobile device goes to market. Many institutes or governments require mobile devices to conform with their stated specifications and protocols to make sure the mobile device will not harm users' health and are compatible with devices from other manufacturers. Once the mobile device passes all checks, a certification will be issued for it.