These are terms that are often used interchangeably, but which may also refer to specific processes in a health insurance or healthcare context.
1) Most commonly, "preauthorization" and "precertification" refer to the process by which a patient is pre-approved for coverage of a specific medical procedure or prescription drug. Health insurance companies may require that patients meet certain criteria before they will extend coverage for some surgeries or for certain drugs. In order to pre-approve such a drug or service, the insurance company will generally require that the patient's doctor submit notes and/or lab results documenting the patient's condition and treatment history.
2) The term "precertification" may also be used to the process by which a hospital notifies a health insurance company of a patient's inpatient admission. This may also be referred to as "pre-admission authorization."
Please note that definitions of terms and plan designs can vary across insurance companies.