but when you fly as authorized instructor then you log everything the landings I mean the same way as the students logs it?
Obviously you're not flying in Afghanistan.
The regulations applicable to your question depend on the jurisdiction in which you intend to fly. In order to get a correct answer, you'll need to be specific. You mentioned the FAA, CAA, and that you're flying in the Philippines. Are you seeking Philippine regulation, FAA regulation, or some other regulation or air legislation/law?