Full searches are just that, they are full searches of you and your person.
These can be done when police have Probable Cause. Probable Cause can be gained in many ways – sometimes Probable Cause can be gained through a Frisk that was undertaken due to Reasonable Suspicion.
Probable Cause from the Fourth Amendment: The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
TLDR: You can be searched fully when it is clear you have committed a crime and charges can be laid, or a warrant placed. There are other circumstances that allow for a full search of your person, but the topic is too broad for here.