Certification involves the testing and evaluation of the technical and nontechnical security features of an IT system to determine its compliance with a set of specified security requirements. Accreditation is a process whereby a Designated Approval Authority (DAA) or other authorizing management official authorizes an IT system to operate for a specific purpose using a defined set of safeguards at an acceptable level of risk.
NIST SP 800-47
A comprehensive assessment of the management, operational, and technical security controls in an information system, made in support of security accreditation, to determine the extent to which the controls are implemented correctly, operating as intended, and producing the desired outcome with respect to meeting the security requirements for the system. Accreditation is the official management decision given by a senior agency official to authorize operation of an information system and to explicitly accept the risk to agency operations (including mission, functions, image, or reputation), agency assets, or individuals, based on the implementation of an agreed-upon set of security controls.
NIST SP 800-64 Rev. 2
(NIST SP 800-37)