How do a school's administrator's search and seizure rights differ from those of a law enforcement officer?

When a child comes to school the school acts in lieu of the parent. If there is a "reasonable doubt" that the child has something that will harm others or himself the school can search for it. The courts have ruled that there has to be a pretty good reason to search and the search has to be reasonable. For instance, if a drug dog shows that there are drugs in a locker or on a student that would be a reasonable search. The student could be asked to turn his/her pockets out or open a locker. Most schools will call in an local officer to do the search and call the parents to inform them that there is a problem. To answer your question in both cases there has to a "reasonable" doubt established for a search.